Evaluate square root of 64/100

$\sqrt{\frac{64}{100}}$

Step 1

Cancel the common factor of $64$ and $100$ .

Factor $4$ out of $64$ .

$\sqrt{\frac{4 (16)}{100}}$

Cancel the common factors.

Factor $4$ out of $100$ .

$\sqrt{\frac{4 \cdot 16}{4 \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{4 \cdot 16}{4 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{16}{25}}$

Step 2

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$\frac{\sqrt{16}}{\sqrt{25}}$

Step 3

Simplify the numerator.

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

$\frac{\sqrt{4^{2}}}{\sqrt{25}}$

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

$\frac{4}{\sqrt{25}}$

Step 4

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$\frac{4}{\sqrt{5^{2}}}$

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

$\frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$