Simplify the Radical Expression ( square root of 2)/( square root of 32)

$\frac{\sqrt{2}}{\sqrt{32}}$

Step 1

Combine $\sqrt{2}$ and $\sqrt{32}$ into a single radical.

$\sqrt{\frac{2}{32}}$

Step 2

Cancel the common factor of $2$ and $32$ .

Factor $2$ out of $2$ .

$\sqrt{\frac{2 (1)}{32}}$

Cancel the common factors.

Factor $2$ out of $32$ .

$\sqrt{\frac{2 \cdot 1}{2 \cdot 16}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 1}{2 \cdot 16}}$

Rewrite the expression.

$\sqrt{\frac{1}{16}}$

Step 3

Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

$\frac{\sqrt{1}}{\sqrt{16}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{16}}$

Step 5

Simplify the denominator.

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

$\frac{1}{\sqrt{4^{2}}}$

Pull terms out from under the radical.

$\frac{1}{| 4 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{1}{4}$