Basic Math Examples

$\sqrt{32 a} \cdot \sqrt{2 a}$

Step 1

Rewrite $32 a$ as ${(2^{2})}^{2} \cdot (2 a)$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) a} \cdot \sqrt{2 a}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

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

Step 1.3

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

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

Step 1.4

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Raise $2$ to the power of $2$ .

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

Step 4

Multiply $4 \sqrt{2 a} \sqrt{2 a}$ .

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Step 4.1

Raise $\sqrt{2 a}$ to the power of $1$ .

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

Step 4.2

Raise $\sqrt{2 a}$ to the power of $1$ .

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

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.4

Add $1$ and $1$ .

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

Step 5

Rewrite ${\sqrt{2 a}}^{2}$ as $2 a$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 a}$ as ${(2 a)}^{\frac{1}{2}}$ .

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

Step 5.2

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

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

Step 5.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

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

Step 5.4.2

Rewrite the expression.

$4 {(2 a)}^{1}$

Step 5.5

Simplify.

$4 (2 a)$

Step 6

Multiply $2$ by $4$ .

$8 a$