Simplify ( square root of 25)÷( square root of 625)

$\sqrt{25} \div \sqrt{625}$

Rewrite the division as a fraction.

$\frac{\sqrt{25}}{\sqrt{625}}$

Combine $\sqrt{25}$ and $\sqrt{625}$ into a single radical.

$\sqrt{\frac{25}{625}}$

Cancel the common factor of $25$ and $625$ .

Factor $25$ out of $25$ .

$\sqrt{\frac{25 (1)}{625}}$

Cancel the common factors.

Factor $25$ out of $625$ .

$\sqrt{\frac{25 \cdot 1}{25 \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{25 \cdot 1}{25 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{1}{25}}$

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$\frac{\sqrt{1}}{\sqrt{25}}$

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{25}}$

Simplify the denominator.

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

$\frac{1}{\sqrt{5^{2}}}$

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

$\frac{1}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$