Simplify square root of 72x- square root of 32x

$\sqrt{72 x} - \sqrt{32 x}$

Step 1

Simplify each term.

Rewrite $72 x$ as $6^{2} \cdot (2 x)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) x} - \sqrt{32 x}$

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

$\sqrt{6^{2} \cdot 2 x} - \sqrt{32 x}$

Add parentheses.

$\sqrt{6^{2} \cdot (2 x)} - \sqrt{32 x}$

$\sqrt{6^{2} \cdot (2 x)} - \sqrt{32 x}$

Pull terms out from under the radical.

$6 \sqrt{2 x} - \sqrt{32 x}$

Rewrite $32 x$ as ${(2^{2})}^{2} \cdot (2 x)$ .

Factor $16$ out of $32$ .

$6 \sqrt{2 x} - \sqrt{16 (2) x}$

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

$6 \sqrt{2 x} - \sqrt{4^{2} \cdot 2 x}$

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

$6 \sqrt{2 x} - (4 \sqrt{2 x})$

Multiply $4$ by $- 1$ .

$6 \sqrt{2 x} - 4 \sqrt{2 x}$

$6 \sqrt{2 x} - 4 \sqrt{2 x}$

Step 2

Subtract $4 \sqrt{2 x}$ from $6 \sqrt{2 x}$ .

$2 \sqrt{2 x}$

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