Basic Math Examples

$\sqrt{3 a} + 6 \sqrt{108} + 3 \sqrt{27 a}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $108$ as $6^{2} \cdot 3$ .

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Step 1.1.1

Factor $36$ out of $108$ .

$\sqrt{3 a} + 6 \sqrt{36 (3)} + 3 \sqrt{27 a}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\sqrt{3 a} + 6 \sqrt{6^{2} \cdot 3} + 3 \sqrt{27 a}$

Step 1.2

Pull terms out from under the radical.

$\sqrt{3 a} + 6 (6 \sqrt{3}) + 3 \sqrt{27 a}$

Step 1.3

Multiply $6$ by $6$ .

$\sqrt{3 a} + 36 \sqrt{3} + 3 \sqrt{27 a}$

Step 1.4

Rewrite $27 a$ as $3^{2} \cdot (3 a)$ .

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Step 1.4.1

Factor $9$ out of $27$ .

$\sqrt{3 a} + 36 \sqrt{3} + 3 \sqrt{9 (3) a}$

Step 1.4.2

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

$\sqrt{3 a} + 36 \sqrt{3} + 3 \sqrt{3^{2} \cdot 3 a}$

Step 1.4.3

Add parentheses.

$\sqrt{3 a} + 36 \sqrt{3} + 3 \sqrt{3^{2} \cdot (3 a)}$

Step 1.5

Pull terms out from under the radical.

$\sqrt{3 a} + 36 \sqrt{3} + 3 (3 \sqrt{3 a})$

Step 1.6

Multiply $3$ by $3$ .

$\sqrt{3 a} + 36 \sqrt{3} + 9 \sqrt{3 a}$

Step 2

Add $\sqrt{3 a}$ and $9 \sqrt{3 a}$ .

$10 \sqrt{3 a} + 36 \sqrt{3}$