Question

Help me answer this also please simply also no decimals and this is Dividing Radicals.
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Answer 1

`\displaystyle (√(2))/(x^2)`

Explanation:

Dividing Radicals

Given the division of radicals:

`\displaystyle (√(Z))/(√(Y))`

We can join both arguments of the radicals into one simple radical as follows:

`\displaystyle \sqrt{(Z)/(Y)}`

We are given the expression:

`\displaystyle 2(√(24))/(√(48x^4))`

Joining them in a single radical:

`\displaystyle 2(√(24))/(√(48x^4))=2\sqrt{(24)/(48x^4)}`

Simplifying the fraction:

`\displaystyle 2\sqrt{(24)/(48x^4)}=2\sqrt{(1)/(2x^4)}`

Multiplying by 2 in numerator and denominator:

`\displaystyle 2\sqrt{(1)/(2x^4)}=2\sqrt{(2)/(4x^4)}`

The denominator is a perfect square:

`\displaystyle 2\sqrt{(2)/(4x^4)}=2(√(2))/(2x^2)`

Simplifying by 2:

`\boxed{\displaystyle (√(2))/(x^2)}`