Evaluate square root of 75/4

$\sqrt{\frac{75}{4}}$

Step 1

Rewrite $\sqrt{\frac{75}{4}}$ as $\frac{\sqrt{75}}{\sqrt{4}}$ .

$\frac{\sqrt{75}}{\sqrt{4}}$

Step 2

Simplify the numerator.

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$\frac{\sqrt{25 (3)}}{\sqrt{4}}$

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

$\frac{\sqrt{5^{2} \cdot 3}}{\sqrt{4}}$

Pull terms out from under the radical.

$\frac{5 \sqrt{3}}{\sqrt{4}}$

Step 3

Simplify the denominator.

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

$\frac{5 \sqrt{3}}{\sqrt{2^{2}}}$

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

$\frac{5 \sqrt{3}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{3}}{2}$

Decimal Form:

$4.33012701 \dots$