Simplify square root of 25/49

$\sqrt{\frac{25}{49}}$

Step 1

Rewrite $\sqrt{\frac{25}{49}}$ as $\frac{\sqrt{25}}{\sqrt{49}}$ .

$\frac{\sqrt{25}}{\sqrt{49}}$

Step 2

Simplify the numerator.

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

$\frac{\sqrt{5^{2}}}{\sqrt{49}}$

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

$\frac{5}{\sqrt{49}}$

Step 3

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{5}{\sqrt{7^{2}}}$

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

$\frac{5}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{7}$

Decimal Form:

$0.\overline{714285}$