Algebra Examples

$\frac{\sqrt{21 x^{12}}}{\sqrt{3 x^{3}}}$

Step 1

Combine $\sqrt{21 x^{12}}$ and $\sqrt{3 x^{3}}$ into a single radical.

$\sqrt{\frac{21 x^{12}}{3 x^{3}}}$

Step 2

Reduce the expression $\frac{21 x^{12}}{3 x^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $21 x^{12}$ .

$\sqrt{\frac{3 (7 x^{12})}{3 x^{3}}}$

Step 2.2

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

$\sqrt{\frac{3 (7 x^{12})}{3 (x^{3})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (7 x^{12})}{3 x^{3}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{7 x^{12}}{x^{3}}}$

Step 3

Cancel the common factor of $x^{12}$ and $x^{3}$ .

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Step 3.1

Factor $x^{3}$ out of $7 x^{12}$ .

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{3} (7 x^{9})}{x^{3} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{7 x^{9}}{1}}$

Step 3.2.4

Divide $7 x^{9}$ by $1$ .

$\sqrt{7 x^{9}}$

Step 4

Rewrite $7 x^{9}$ as ${({(x^{2})}^{2})}^{2} \cdot (7 x)$ .

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Step 4.1

Factor out $x^{8}$ .

$\sqrt{7 (x^{8} x)}$

Step 4.2

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{7 ({(x^{4})}^{2} x)}$

Step 4.3

Reorder $7$ and ${(x^{4})}^{2}$ .

$\sqrt{{(x^{4})}^{2} \cdot 7 x}$

Step 4.4

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

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot 7 x}$

Step 4.5

Add parentheses.

$\sqrt{{({(x^{2})}^{2})}^{2} \cdot (7 x)}$

Step 5

Pull terms out from under the radical.

${(x^{2})}^{2} \sqrt{7 x}$

Step 6

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

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Step 6.1

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

$x^{2 \cdot 2} \sqrt{7 x}$

Step 6.2

Multiply $2$ by $2$ .

$x^{4} \sqrt{7 x}$