Simplify x square root of 150x^5

$x \sqrt{150 x^{5}}$

Step 1

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

Factor $25$ out of $150$ .

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

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

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

Factor out $x^{4}$ .

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

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

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

Move $6$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{2}$ .

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

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

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

$5 (x^{2} x^{1}) \sqrt{6 x}$

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

$5 x^{2 + 1} \sqrt{6 x}$

Add $2$ and $1$ .

$5 x^{3} \sqrt{6 x}$