Simplify 3 square root of 8/512

$3 \sqrt{\frac{8}{512}}$

Step 1

Cancel the common factor of $8$ and $512$ .

Factor $8$ out of $8$ .

$3 \sqrt{\frac{8 (1)}{512}}$

Cancel the common factors.

Factor $8$ out of $512$ .

$3 \sqrt{\frac{8 \cdot 1}{8 \cdot 64}}$

Cancel the common factor.

$3 \sqrt{\frac{8 \cdot 1}{8 \cdot 64}}$

Rewrite the expression.

$3 \sqrt{\frac{1}{64}}$

Step 2

Rewrite $\sqrt{\frac{1}{64}}$ as $\frac{\sqrt{1}}{\sqrt{64}}$ .

$3 \frac{\sqrt{1}}{\sqrt{64}}$

Step 3

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt{64}}$

Step 4

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$3 \frac{1}{\sqrt{8^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$3 (\frac{1}{8})$

Step 5

Combine $3$ and $\frac{1}{8}$ .

$\frac{3}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$