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

2 Answers
mason m
Feb 24, 2016

3-sqrt5

Explanation:

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

Tony B
Feb 26, 2016

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

" "3-sqrt(5)

Explanation:

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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