Algebra Examples

$\frac{3 \sqrt{32 a^{2}}}{\sqrt{8 a}}$

Step 1

Combine $\sqrt{32 a^{2}}$ and $\sqrt{8 a}$ into a single radical.

$3 \sqrt{\frac{32 a^{2}}{8 a}}$

Step 2

Reduce the expression $\frac{32 a^{2}}{8 a}$ by cancelling the common factors.

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Step 2.1

Factor $8$ out of $32 a^{2}$ .

$3 \sqrt{\frac{8 (4 a^{2})}{8 a}}$

Step 2.2

Factor $8$ out of $8 a$ .

$3 \sqrt{\frac{8 (4 a^{2})}{8 (a)}}$

Step 2.3

Cancel the common factor.

$3 \sqrt{\frac{8 (4 a^{2})}{8 a}}$

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $a^{2}$ and $a$ .

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Step 3.1

Factor $a$ out of $4 a^{2}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$3 \sqrt{\frac{a (4 a)}{a^{1}}}$

Step 3.2.2

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

$3 \sqrt{\frac{a (4 a)}{a \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$3 \sqrt{\frac{a (4 a)}{a \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$3 \sqrt{\frac{4 a}{1}}$

Step 3.2.5

Divide $4 a$ by $1$ .

$3 \sqrt{4 a}$

Step 4

Rewrite $4$ as $2^{2}$ .

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

Step 5

Pull terms out from under the radical.

$3 (2 \sqrt{a})$

Step 6

Multiply $2$ by $3$ .

$6 \sqrt{a}$