Simplify x^2 square root of 36x^4y^7

$x^{2} \sqrt{36 x^{4} y^{7}}$

Step 1

Rewrite $36 x^{4} y^{7}$ as ${(6 x^{2} y^{3})}^{2} y$ .

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

$x^{2} \sqrt{6^{2} x^{4} y^{7}}$

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

$x^{2} \sqrt{6^{2} {(x^{2})}^{2} y^{7}}$

Factor out $y^{6}$ .

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

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

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

Rewrite $6^{2} {(x^{2})}^{2} {(y^{3})}^{2}$ as ${(6 x^{2} y^{3})}^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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