Basic Math Examples

$6 \sqrt{108 a} - 4 \sqrt{48 a}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $36$ out of $108$ .

$6 \sqrt{36 (3) a} - 4 \sqrt{48 a}$

Step 1.1.2

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

$6 \sqrt{6^{2} \cdot 3 a} - 4 \sqrt{48 a}$

Step 1.1.3

Add parentheses.

$6 \sqrt{6^{2} \cdot (3 a)} - 4 \sqrt{48 a}$

Step 1.2

Pull terms out from under the radical.

$6 (6 \sqrt{3 a}) - 4 \sqrt{48 a}$

Step 1.3

Multiply $6$ by $6$ .

$36 \sqrt{3 a} - 4 \sqrt{48 a}$

Step 1.4

Rewrite $48 a$ as ${(2^{2})}^{2} \cdot (3 a)$ .

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Step 1.4.1

Factor $16$ out of $48$ .

$36 \sqrt{3 a} - 4 \sqrt{16 (3) a}$

Step 1.4.2

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

$36 \sqrt{3 a} - 4 \sqrt{4^{2} \cdot 3 a}$

Step 1.4.3

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

$36 \sqrt{3 a} - 4 \sqrt{{(2^{2})}^{2} \cdot 3 a}$

Step 1.4.4

Add parentheses.

$36 \sqrt{3 a} - 4 \sqrt{{(2^{2})}^{2} \cdot (3 a)}$

Step 1.5

Pull terms out from under the radical.

$36 \sqrt{3 a} - 4 (2^{2} \sqrt{3 a})$

Step 1.6

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

$36 \sqrt{3 a} - 4 (4 \sqrt{3 a})$

Step 1.7

Multiply $4$ by $- 4$ .

$36 \sqrt{3 a} - 16 \sqrt{3 a}$

Step 2

Subtract $16 \sqrt{3 a}$ from $36 \sqrt{3 a}$ .

$20 \sqrt{3 a}$