Algebra Examples

$\sqrt{8 a^{3}} \div \sqrt{2 a}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{8 a^{3}}}{\sqrt{2 a}}$

Step 2

Combine $\sqrt{8 a^{3}}$ and $\sqrt{2 a}$ into a single radical.

$\sqrt{\frac{8 a^{3}}{2 a}}$

Step 3

Reduce the expression $\frac{8 a^{3}}{2 a}$ by cancelling the common factors.

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Step 3.1

Factor $2$ out of $8 a^{3}$ .

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

Step 3.2

Factor $2$ out of $2 a$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$\sqrt{\frac{4 a^{3}}{a}}$

Step 4

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

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Step 4.1

Factor $a$ out of $4 a^{3}$ .

$\sqrt{\frac{a (4 a^{2})}{a}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\sqrt{\frac{a (4 a^{2})}{a^{1}}}$

Step 4.2.2

Factor $a$ out of $a^{1}$ .

$\sqrt{\frac{a (4 a^{2})}{a \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt{\frac{a (4 a^{2})}{a \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt{\frac{4 a^{2}}{1}}$

Step 4.2.5

Divide $4 a^{2}$ by $1$ .

$\sqrt{4 a^{2}}$

Step 5

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

$\sqrt{{(2 a)}^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$2 a$