How do you simplify square root of 128 + the square root of 32?

Answer 1

#12sqrt2#

Simplify:

#sqrt128=sqrt16xxsqrt8 -> 4 xx sqrt4 xx sqrt2=8sqrt2#.
#sqrt32=sqrt16xxsqrt2=4sqrt2#
#8sqrt2+4sqrt2=12sqrt2#
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Answer 2
#sqrt(128)+sqrt(32)#
#sqrt((4 xx 4) xx (2 xx 2) xx 2) + sqrt((4 xx 4) xx 2)#
#4 xx 2sqrt(2) + 4sqrt(2)#
#8sqrt(2) + 4sqrt(2)#
#12sqrt(2)#
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Answer 3

#\sqrt(128)+\sqrt(32)=2*\sqrt(12)#

#\sqrt(128)+\sqrt(32)#
Write both numbers as a product of prime numbers.
(unique factorisation ).

For example:

#128=2*64=2*2*32#
#32=2*16=2*2*8=2*2*2*4=2^5=2^4*2#

#\sqrt(128)+\sqrt(32)=\sqrt(2*2*32)+\sqrt(32)=#
#=\sqrt(2*2)* \sqrt(32)+\sqrt(32)=2* \sqrt(32)+\sqrt(32)=#
#=3*\sqrt(32)=3* \sqrt(2^4*2)= 3*\sqrt(2^4)*\sqrt(2)= 3*2^2*\sqrt(2)=#
#=3*4*\sqrt(2)=12\sqrt(2)#

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Answer 4

#12sqrt(2)#

Given: #sqrt(128)+sqrt(32)#

You are looking for squared values that you can 'extract' from the roots.

If you are ever not sure do a quick sketch of a prime factor tree to help:

#sqrt(128)+sqrt(32)#

#sqrt(2^2xx2^2xx2^2xx2)+sqrt(2^2xx2^2xx2)#

#color(white)("ddddd")8sqrt(2)color(white)("dddddd")+color(white)("dddd")4sqrt(2)color(white)("dddd")=color(white)("d")12sqrt(2)#

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Answer 5

To simplify √128 + √32, we can break down the numbers into their prime factors and simplify the square roots separately.

√128 = √(2^7) = 2^3√2 = 8√2 √32 = √(2^5) = 2^2√2 = 4√2

Therefore, √128 + √32 simplifies to 8√2 + 4√2, which can be further simplified as (8 + 4)√2 = 12√2.

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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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