Question

Which expression is equivalent to

Answer 1

Answer:

$\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}$

Step-by-step explanation:

Given

$\sqrt{128x^8y^3}$ --- the complete expression

Required

The equivalent expression

We have:

$\sqrt{128x^8y^3}$

Expand

$\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}$

Further expand

$\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}$

Rewrite as:

$\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}$

Split

$\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}$

Express as:

$\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}$

Remove bracket

$\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}$

$\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}$

$\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}$

$\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}$