What is #sqrt192# in simplest radical form? Thanks!

I need help checking my extra work for practice and wanted to know how to do #sqrt192# as well as the simplest answer in radical form. The answer I got was #8sqrt3# if this is not the correct answer, please let me know why. If it is, let me know that I am correct so I don't have to worry about failing my math test in a couple of weeks. Thanks!

Answer 1

#sqrt(192) = 8sqrt(3)#

You have the right answer. Here's why.

If #a, b >= 0# then:
#sqrt(ab) = sqrt(a)sqrt(b)#
If #a >= 0# then:
#sqrt(a^2) = a#
Find the prime factorisation of #192# and identify square factors:
#192 = 2*2*2*2*2*2*3 = 2^6*3 = (2^3)^2*3 = 8^2*3#

So:

#sqrt(192) = sqrt(8^2*3) = sqrt(8^2)*sqrt(3) = 8sqrt(3)#
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Answer 2

( \sqrt{192} ) in simplest radical form is ( 8\sqrt{3} ).

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Answer 3

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(( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( ( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrtTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 =( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

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[ \sqrt{192}To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times ( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times ( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3}To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times ( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

SoTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So,To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, (To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192}( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrtTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192}To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as (( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} )To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) inTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplestTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radicalTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical formTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form isTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is (To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times ( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3}( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrtTo simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3}To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using the property (( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3} ).To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using the property ( \( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3} ).To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using the property ( \sqrt( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3} ).To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using the property ( \sqrt{( \sqrt{192} ) in simplest radical form can be simplified by factoring out perfect square factors from 192:

[ \sqrt{192} = \sqrt{64 \times 3} ]

[ = \sqrt{64} \times \sqrt{3} ]

[ = 8 \sqrt{3} ]

So, ( \sqrt{192} ) in simplest radical form is ( 8 \sqrt{3} ).To simplify ( \sqrt{192} ) in radical form, first, factor 192 into its prime factors.

( 192 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3 )

Now, we can rewrite ( \sqrt{192} ) as ( \sqrt{2^5 \times 3} ).

Using the property ( \sqrt{ab} = \sqrt{a} \times \sqrt{b} ), we can split the square root:

( \sqrt{192} = \sqrt{2^5 \times 3} = \sqrt{2^5} \times \sqrt{3} )

( = \sqrt{32} \times \sqrt{3} )

Now, ( \sqrt{32} ) can be simplified further. Since ( 32 = 16 \times 2 ), we have:

( \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2} )

So, ( \sqrt{192} ) in simplest radical form is ( 4 \sqrt{2} \times \sqrt{3} ), which can also be written as ( 4\sqrt{6} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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