Question

Simplify:

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$

Short answer

The simplification of $\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$is $4xy\sqrt{3x}$

Step-by-step solution

Step 1. Given

An expression$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}$

To simplify the expression

Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}=\sqrt{\frac{64x^4{y}^5}{2x{y}^3}}$

Remove the common factors.

$=\sqrt{48x^3{y}^2}$

Step 3. Rewrite the radical as the product of two radicals.

$\frac{\sqrt{64x^4{y}^5}}{\sqrt{2x{y}^3}}=\sqrt{48x^3{y}^2}$

$=\sqrt{16x^2{y}^2}\sqrt{3x}$

$=4xy\sqrt{3x}$

The simplification of the expression is $4xy\sqrt{3x}$