Basic Math Examples

$\sqrt{64 a} + \sqrt{25 a} + \sqrt{81 a}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} a} + \sqrt{25 a} + \sqrt{81 a}$

Step 1.2

Pull terms out from under the radical.

$8 \sqrt{a} + \sqrt{25 a} + \sqrt{81 a}$

Step 1.3

Rewrite $25$ as $5^{2}$ .

$8 \sqrt{a} + \sqrt{5^{2} a} + \sqrt{81 a}$

Step 1.4

Pull terms out from under the radical.

$8 \sqrt{a} + 5 \sqrt{a} + \sqrt{81 a}$

Step 1.5

Rewrite $81 a$ as ${(3^{2})}^{2} a$ .

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Step 1.5.1

Rewrite $81$ as $9^{2}$ .

$8 \sqrt{a} + 5 \sqrt{a} + \sqrt{9^{2} a}$

Step 1.5.2

Rewrite $9$ as $3^{2}$ .

$8 \sqrt{a} + 5 \sqrt{a} + \sqrt{{(3^{2})}^{2} a}$

$8 \sqrt{a} + 5 \sqrt{a} + \sqrt{{(3^{2})}^{2} a}$

Step 1.6

Pull terms out from under the radical.

$8 \sqrt{a} + 5 \sqrt{a} + 3^{2} \sqrt{a}$

Step 1.7

Raise $3$ to the power of $2$ .

$8 \sqrt{a} + 5 \sqrt{a} + 9 \sqrt{a}$

$8 \sqrt{a} + 5 \sqrt{a} + 9 \sqrt{a}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $8 \sqrt{a}$ and $5 \sqrt{a}$ .

$13 \sqrt{a} + 9 \sqrt{a}$

Step 2.2

Add $13 \sqrt{a}$ and $9 \sqrt{a}$ .

$22 \sqrt{a}$

$22 \sqrt{a}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$