How do you simplify #(6-sqrt20) / 2#?

Answer 1

#3-sqrt5#

First, recognize that we can simplify #sqrt20#, since #20=4xx5#.

We can split up a square root through the rule that

#sqrt(axxb)=sqrtasqrtb#

So,

#sqrt20=sqrt(4xx5)=sqrt4sqrt5=2sqrt5#

Thus, the expression equals

#(6-2sqrt5)/2#

We can split up the fraction:

#6/2-(2sqrt5)/2#

Which equals

#3-sqrt5#
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Answer 2

A very slight variation in presentation. Also written with a lot of detail about each step.

#" "3-sqrt(5)#

Looking for common factors. 6 and 20 are even so have a factor of 2. As the denominator is 2 as well we have a first step in simplification

Write as: #" " 6/2 -sqrt(20)/2#
#" "(2xx3)/2-(sqrt(2xx10))/2#
But #2xx5 = 10# so we now have
#" "((2xx3)/2)-((sqrt(2^2xx5))/2)#
#" "(2/2 xx 3)-((2sqrt(5))/2)#
#" "(1 xx 3) -(2/2xxsqrt(5))#
#" "(1 xx 3) -(1xxsqrt(5))#
#" "3-sqrt(5)#
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Answer 3

To simplify (6 - √20) / 2, we can first simplify the square root of 20. The square root of 20 can be simplified as √(4 × 5), which is equal to 2√5. Therefore, the expression becomes (6 - 2√5) / 2. We can further simplify this by dividing each term by 2, resulting in 3 - √5.

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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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