Simplify y^3 square root of 20x^5y^4

$y^{3} \sqrt{20 x^{5} y^{4}}$

Step 1

Rewrite $20 x^{5} y^{4}$ as ${(2 x^{2} y^{2})}^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$y^{3} \sqrt{4 (5) x^{5} y^{4}}$

Rewrite $4$ as $2^{2}$ .

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

Factor out $x^{4}$ .

$y^{3} \sqrt{2^{2} \cdot 5 (x^{4} x) y^{4}}$

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

$y^{3} \sqrt{2^{2} \cdot 5 ({(x^{2})}^{2} x) y^{4}}$

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

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

Move $x$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $y^{2}$ .

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

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

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

Add $2$ and $3$ .

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

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