Question

What is the simplest form of square root of

Answer 1

`image`

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Answer 2

First step is to simplify the inside of the radical. There are x's on both top and bottom of the fraction. So we subtract their exponents. x³ - x¹ = x². Because the x³ was in the denominator and it was bigger, the x² goes on the bottom.

Your new equation is:

`\sqrt{(126y^(5))/(32x^(2)) }`

Now, I'd suggest factoring each term to correspond with the square root.

126y⁵ = 9 · 14 · y² · y² · y

32x² = 4 · 4 · 2 · x²

9, y², and y² can be square rooted in the numerator. 4, 4, and x² in the denominator. So we pull out their square roots and place them outside of the radical. The rest stays in the radical:

`(3 * y * y)/(2*2*x)\sqrt{(14y)/(2)}`

Simplify to get your final answer:

`(3y^(2))/(4x) √(7y)`

It's easier to explain on paper and in person than over computer text, sadly. Hopefully you can follow along with this.