What is the possible answer for sqrt2x(sqrt8x-sqrt32)? How to simplify the answer too?

sqrt2x(sqrt8x-sqrt32)

2 Answers
Sep 26, 2017

sqrt(2) sqrt(x) (2sqrt(2)sqrt(x) - 4sqrt(2))

Explanation:

color(red)(root(n)(ab) = root(n)(a) * root(n)(b))

sqrt(2x) must have been the result of:
sqrt(2) * sqrt(x)

Now that's out of the way, using the same logic:
How did they get sqrt(8x) ?

Pull it apart and you get:
sqrt(8) = 2sqrt(2) and sqrt(x)

Same thing here: sqrt(32) = 4sqrt(2)

After picking apart everything we get:

color(red)(sqrt(2x)(sqrt(8x) - sqrt(32))) = ...
sqrt(2) sqrt(x) (2sqrt(2)sqrt(x) - 4sqrt(2))

Simplifying:
color(red)(a(b+c) = ab+ac

(sqrt(2)sqrt(x) * 2sqrt(2)sqrt(x)) - (sqrt(2)sqrt(x) * 4sqrt(2))

sqrt(2)sqrt(x) * 2sqrt(2)sqrt(x) = 4x

sqrt(2)sqrt(x) * 4sqrt(2) = 8sqrt(x)

4x - 8sqrt(x)

Sep 26, 2017

Given
sqrt(2) x (sqrt(8)x - sqrt(32))

Let us take sqrt2 inside the parentheses and multiply both terms. It becomes

x (sqrt2xxsqrt8x - sqrt2xxsqrt(32))
=>x (sqrt(8xx2)x - sqrt(32xx2))
=>x (sqrt(16)x - sqrt(64))
=>x (4x - 8)

Taking common factor 4 outside the parentheses we get simplified form as

4x (x - 2)