Simplify square root of 54x- square root of 24x

$\sqrt{54 x} - \sqrt{24 x}$

Step 1

Simplify each term.

Rewrite $54 x$ as $3^{2} \cdot (6 x)$ .

Factor $9$ out of $54$ .

$\sqrt{9 (6) x} - \sqrt{24 x}$

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

$\sqrt{3^{2} \cdot 6 x} - \sqrt{24 x}$

Add parentheses.

$\sqrt{3^{2} \cdot (6 x)} - \sqrt{24 x}$

$\sqrt{3^{2} \cdot (6 x)} - \sqrt{24 x}$

Pull terms out from under the radical.

$3 \sqrt{6 x} - \sqrt{24 x}$

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

Factor $4$ out of $24$ .

$3 \sqrt{6 x} - \sqrt{4 (6) x}$

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

$3 \sqrt{6 x} - (2 \sqrt{6 x})$

Multiply $2$ by $- 1$ .

$3 \sqrt{6 x} - 2 \sqrt{6 x}$

$3 \sqrt{6 x} - 2 \sqrt{6 x}$

Step 2

Subtract $2 \sqrt{6 x}$ from $3 \sqrt{6 x}$ .

$\sqrt{6 x}$

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