Evaluate square root of 28/25

$\sqrt{\frac{28}{25}}$

Step 1

Rewrite $\sqrt{\frac{28}{25}}$ as $\frac{\sqrt{28}}{\sqrt{25}}$ .

$\frac{\sqrt{28}}{\sqrt{25}}$

Step 2

Simplify the numerator.

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$\frac{\sqrt{4 (7)}}{\sqrt{25}}$

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

$\frac{\sqrt{2^{2} \cdot 7}}{\sqrt{25}}$

Pull terms out from under the radical.

$\frac{2 \sqrt{7}}{\sqrt{25}}$

Step 3

Simplify the denominator.

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

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.05830052 \dots$