Simplify the Radical Expression ( square root of 270x^5)/( square root of 10)

$\frac{\sqrt{270 x^{5}}}{\sqrt{10}}$

Step 1

Combine $\sqrt{270 x^{5}}$ and $\sqrt{10}$ into a single radical.

$\sqrt{\frac{270 x^{5}}{10}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{270 x^{5}}{10}$ by cancelling the common factors.

Factor $10$ out of $270 x^{5}$ .

$\sqrt{\frac{10 (27 x^{5})}{10}}$

Factor $10$ out of $10$ .

$\sqrt{\frac{10 (27 x^{5})}{10 (1)}}$

Cancel the common factor.

$\sqrt{\frac{10 (27 x^{5})}{10 \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{27 x^{5}}{1}}$

Divide $27 x^{5}$ by $1$ .

$\sqrt{27 x^{5}}$

Step 3

Rewrite $27 x^{5}$ as ${(3 x^{2})}^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x^{5}}$

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{4}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$| 3 x^{2} | \sqrt{3 x}$

Step 5

Remove non-negative terms from the absolute value.

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