Solve sqrt{5-(frac{sqrt{15}}{2})^2}

$$\sqrt { 5 - ( \frac { \sqrt { 15 } } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

To raise \frac{\sqrt{15}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{5-\frac{\left(\sqrt{15}\right)^{2}}{2^{2}}}$$

The square of \sqrt{15} is 15.

$$\sqrt{5-\frac{15}{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{5-\frac{15}{4}}$$

Subtract \frac{15}{4} from 5 to get \frac{5}{4}.

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

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

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

Calculate the square root of 4 and get 2.

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