Evaluate square root of 20/49

$\sqrt{\frac{20}{49}}$

Step 1

Rewrite $\sqrt{\frac{20}{49}}$ as $\frac{\sqrt{20}}{\sqrt{49}}$ .

$\frac{\sqrt{20}}{\sqrt{49}}$

Step 2

Simplify the numerator.

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$\frac{\sqrt{4 (5)}}{\sqrt{49}}$

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

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

Pull terms out from under the radical.

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

Step 3

Simplify the denominator.

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

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.63887656 \dots$