Algebra Examples

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

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.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Factor $10$ out of $10$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

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

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

Step 3

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

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Step 3.1

Factor $9$ out of $27$ .

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

Step 3.2

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

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

Step 3.3

Factor out $x^{4}$ .

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

Step 3.4

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

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

Step 3.5

Move $3$ .

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

Step 3.6

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

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

Step 3.7

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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