Simplify 6 square root of 108a-4 square root of 48a

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

Step 1

Simplify each term.

Rewrite

$108 a$ as

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

Factor

$36$ out of

$108$ .

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

Rewrite

$36$ as

$6^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply

$6$ by

$6$ .

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

Rewrite

$48 a$ as

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

Factor

$16$ out of

$48$ .

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

Rewrite

$16$ as

$4^{2}$ .

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

Rewrite

$4$ as

$2^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Raise

$2$ to the power of

$2$ .

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

Multiply

$4$ by

$- 4$ .

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

Step 2

Subtract

$16 \sqrt{3 a}$ from

$36 \sqrt{3 a}$ .

$20 \sqrt{3 a}$

Simplify 6 square root of 108a-4 square root of 48a

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