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

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

Step 1

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

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

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

Factor out $x^{4}$ .

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

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

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

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

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

Move $x$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$6 (x^{2} x^{1}) (y^{2} \sqrt{x})$

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

$6 x^{2 + 1} (y^{2} \sqrt{x})$

Add $2$ and $1$ .

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

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