Simplify square root of 27x- square root of 12x

$\sqrt{27 x} - \sqrt{12 x}$

Step 1

Simplify each term.

Rewrite $27 x$ as $3^{2} \cdot (3 x)$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3) x} - \sqrt{12 x}$

Rewrite $9$ as $3^{2}$ .

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Factor $4$ out of $12$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

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

$\sqrt{3 x}$

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