Simplify square root of 48x- square root of 12x

$\sqrt{48 x} - \sqrt{12 x}$

Simplify each term.

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

Factor $16$ out of $48$ .

$\sqrt{16 (3) x} - \sqrt{12 x}$

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

$\sqrt{4^{2} \cdot 3 x} - \sqrt{12 x}$

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

$\sqrt{{(2^{2})}^{2} \cdot 3 x} - \sqrt{12 x}$

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (3 x)} - \sqrt{12 x}$

$\sqrt{{(2^{2})}^{2} \cdot (3 x)} - \sqrt{12 x}$

Pull terms out from under the radical.

$2^{2} \sqrt{3 x} - \sqrt{12 x}$

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

$4 \sqrt{3 x} - \sqrt{12 x}$

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

Factor $4$ out of $12$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

$4 \sqrt{3 x} - (2 \sqrt{3 x})$

Multiply $2$ by $- 1$ .

$4 \sqrt{3 x} - 2 \sqrt{3 x}$

$4 \sqrt{3 x} - 2 \sqrt{3 x}$

Subtract $2 \sqrt{3 x}$ from $4 \sqrt{3 x}$ .

$2 \sqrt{3 x}$

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