Simplify square root of 32x- square root of 8x

$\sqrt{32 x} - \sqrt{8 x}$

Step 1

Simplify each term.

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

Factor $16$ out of $32$ .

$\sqrt{16 (2) x} - \sqrt{8 x}$

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

$\sqrt{4^{2} \cdot 2 x} - \sqrt{8 x}$

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

$\sqrt{{(2^{2})}^{2} \cdot 2 x} - \sqrt{8 x}$

Add parentheses.

$\sqrt{{(2^{2})}^{2} \cdot (2 x)} - \sqrt{8 x}$

$\sqrt{{(2^{2})}^{2} \cdot (2 x)} - \sqrt{8 x}$

Pull terms out from under the radical.

$2^{2} \sqrt{2 x} - \sqrt{8 x}$

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

$4 \sqrt{2 x} - \sqrt{8 x}$

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

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

Step 2

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

$2 \sqrt{2 x}$

Related Questions