Pre-Algebra Examples

$\frac{\sqrt{9 x^{13}}}{\sqrt{12 x^{5}}}$

Step 1

Combine $\sqrt{9 x^{13}}$ and $\sqrt{12 x^{5}}$ into a single radical.

$\sqrt{\frac{9 x^{13}}{12 x^{5}}}$

Step 2

Reduce the expression $\frac{9 x^{13}}{12 x^{5}}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $3$ out of $9 x^{13}$ .

$\sqrt{\frac{3 (3 x^{13})}{12 x^{5}}}$

Step 2.2

Factor $3$ out of $12 x^{5}$ .

$\sqrt{\frac{3 (3 x^{13})}{3 (4 x^{5})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (3 x^{13})}{3 (4 x^{5})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{3 x^{13}}{4 x^{5}}}$

Step 3

Cancel the common factor of $x^{13}$ and $x^{5}$ .

Tap for more steps...

Step 3.1

Factor $x^{5}$ out of $3 x^{13}$ .

$\sqrt{\frac{x^{5} (3 x^{8})}{4 x^{5}}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $x^{5}$ out of $4 x^{5}$ .

$\sqrt{\frac{x^{5} (3 x^{8})}{x^{5} \cdot 4}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{5} (3 x^{8})}{x^{5} \cdot 4}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{3 x^{8}}{4}}$

Step 4

Rewrite $\frac{3 x^{8}}{4}$ as ${(\frac{{(x^{2})}^{2}}{2})}^{2} \cdot 3$ .

Tap for more steps...

Step 4.1

Factor the perfect power ${({(x^{2})}^{2})}^{2}$ out of $3 x^{8}$ .

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

Step 4.2

Factor the perfect power $2^{2}$ out of $4$ .

$\sqrt{\frac{{({(x^{2})}^{2})}^{2} \cdot 3}{2^{2} \cdot 1}}$

Step 4.3

Rearrange the fraction $\frac{{({(x^{2})}^{2})}^{2} \cdot 3}{2^{2} \cdot 1}$ .

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

Step 5

Pull terms out from under the radical.

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

Step 6

Multiply the exponents in ${(x^{2})}^{2}$ .

Tap for more steps...

Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 6.2

Multiply $2$ by $2$ .

$\frac{x^{4}}{2} \sqrt{3}$

Step 7

Combine $\frac{x^{4}}{2}$ and $\sqrt{3}$ .

$\frac{x^{4} \sqrt{3}}{2}$