Simplify square root of 75x- square root of 48x

$\sqrt{75 x} - \sqrt{48 x}$

Step 1

Simplify each term.

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

Factor $25$ out of $75$ .

$\sqrt{25 (3) x} - \sqrt{48 x}$

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

$\sqrt{5^{2} \cdot 3 x} - \sqrt{48 x}$

Add parentheses.

$\sqrt{5^{2} \cdot (3 x)} - \sqrt{48 x}$

$\sqrt{5^{2} \cdot (3 x)} - \sqrt{48 x}$

Pull terms out from under the radical.

$5 \sqrt{3 x} - \sqrt{48 x}$

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

Factor $16$ out of $48$ .

$5 \sqrt{3 x} - \sqrt{16 (3) x}$

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

$5 \sqrt{3 x} - \sqrt{4^{2} \cdot 3 x}$

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

$5 \sqrt{3 x} - (4 \sqrt{3 x})$

Multiply $4$ by $- 1$ .

$5 \sqrt{3 x} - 4 \sqrt{3 x}$

$5 \sqrt{3 x} - 4 \sqrt{3 x}$

Step 2

Subtract $4 \sqrt{3 x}$ from $5 \sqrt{3 x}$ .

$\sqrt{3 x}$

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