solve the radical expression step by step:

Question

√81x⁵y³z⁸

Answer 1

Sqrt (81x⁵y³z⁸ )

= sqrt ( 9 *9 * x⁵y³z⁸ )

= 9 x ^5/2 *y ^3/2 *z ^8/2

= 9 x ^5/2 *y ^3/2 *z ⁴

Answer 2

NOTE: I am not sure what form they want this answer in. I will break it down into a couple formats.

If I am seeing this correctly, it is the square root of 81x⁵y³z⁸

We can do each term separately: 81, x⁵, y³, and z⁸

The square root of 81 is 9.

When we square root variables, we simply divide the power, or exponent, by 2.

The square root of x⁵ is x^5/2

The square root of y³ is y^3/2

The square root of z⁸ is z^4/2, or z²

If they are okay with having the answer in this format, then your final answer could be

Possible Answer #1: 9x^5/2y^3/2z²

However, this is a bit awkward, so if they want to separate radicals from non-radicals, let's convert the exponents to improper fractions:

x^5/2 = x^{2 1/2}

y^3/2 = y^{1 1/2}

z^4/2 = z²

Let's split the terms that have improper fractions.

A couple key things to note:

* Remember that x^(a+b) = x^a * x^b

* x^1/2 is the same as √x

x^{2 1/2} = x² * x^1/2, or x²√x

y^{1 1/2} = y * y^1/2, or y√y

z² = z²

Let's take the terms that we have now, 9, x²√x, y√y, z², and combine terms: Non-square root terms together, and square root terms together:

Possible Answer #2: 9x²yz²√xy