Simplify 7 square root of 108x-6 square root of 75x

$7 \sqrt{108 x} - 6 \sqrt{75 x}$

Step 1

Simplify each term.

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

Factor $36$ out of $108$ .

$7 \sqrt{36 (3) x} - 6 \sqrt{75 x}$

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

$7 \sqrt{6^{2} \cdot 3 x} - 6 \sqrt{75 x}$

Add parentheses.

$7 \sqrt{6^{2} \cdot (3 x)} - 6 \sqrt{75 x}$

$7 \sqrt{6^{2} \cdot (3 x)} - 6 \sqrt{75 x}$

Pull terms out from under the radical.

$7 (6 \sqrt{3 x}) - 6 \sqrt{75 x}$

Multiply $6$ by $7$ .

$42 \sqrt{3 x} - 6 \sqrt{75 x}$

Rewrite $75 x$ as $5^{2} \cdot (3 x)$ .

Factor $25$ out of $75$ .

$42 \sqrt{3 x} - 6 \sqrt{25 (3) x}$

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

$42 \sqrt{3 x} - 6 \sqrt{5^{2} \cdot 3 x}$

Add parentheses.

$42 \sqrt{3 x} - 6 \sqrt{5^{2} \cdot (3 x)}$

$42 \sqrt{3 x} - 6 \sqrt{5^{2} \cdot (3 x)}$

Pull terms out from under the radical.

$42 \sqrt{3 x} - 6 (5 \sqrt{3 x})$

Multiply $5$ by $- 6$ .

$42 \sqrt{3 x} - 30 \sqrt{3 x}$

$42 \sqrt{3 x} - 30 \sqrt{3 x}$

Step 2

Subtract $30 \sqrt{3 x}$ from $42 \sqrt{3 x}$ .

$12 \sqrt{3 x}$

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