Simplify x^2 square root of 150x^5y^4

$x^{2} \sqrt{150 x^{5} y^{4}}$

Step 1

Rewrite $150 x^{5} y^{4}$ as ${(5 x^{2} y^{2})}^{2} \cdot (6 x)$ .

Factor $25$ out of $150$ .

$x^{2} \sqrt{25 (6) x^{5} y^{4}}$

Rewrite $25$ as $5^{2}$ .

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

Factor out $x^{4}$ .

$x^{2} \sqrt{5^{2} \cdot 6 (x^{4} x) y^{4}}$

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

$x^{2} \sqrt{5^{2} \cdot 6 ({(x^{2})}^{2} x) y^{4}}$

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

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

Move $x$ .

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

Move $6$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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