Simplify y^3 square root of 36x^4y^5

$y^{3} \sqrt{36 x^{4} y^{5}}$

Step 1

Rewrite $36 x^{4} y^{5}$ as ${(6 x^{2} y^{2})}^{2} y$ .

Rewrite $36$ as $6^{2}$ .

$y^{3} \sqrt{6^{2} x^{4} y^{5}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$y^{3} \sqrt{6^{2} {(x^{2})}^{2} y^{5}}$

Factor out $y^{4}$ .

$y^{3} \sqrt{6^{2} {(x^{2})}^{2} (y^{4} y)}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$y^{3} \sqrt{6^{2} {(x^{2})}^{2} ({(y^{2})}^{2} y)}$

Rewrite $6^{2} {(x^{2})}^{2} {(y^{2})}^{2}$ as ${(6 x^{2} y^{2})}^{2}$ .

$y^{3} \sqrt{{(6 x^{2} y^{2})}^{2} y}$

Step 2

Pull terms out from under the radical.

$y^{3} (6 x^{2} y^{2} \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$6 y^{3} (x^{2} y^{2} \sqrt{y})$

Step 4

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$6 (y^{2} y^{3}) (x^{2} \sqrt{y})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 y^{2 + 3} (x^{2} \sqrt{y})$

Add $2$ and $3$ .

$6 y^{5} (x^{2} \sqrt{y})$

$6 y^{5} x^{2} \sqrt{y}$