Solve sqrt{6^2-(5/2)^2}

$$\sqrt { 6 ^ { 2 } - ( \frac { 5 } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{119}}{2}\approx 5.454356057$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36-\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\sqrt{36-\frac{25}{4}}$$

Convert 36 to fraction \frac{144}{4}.

$$\sqrt{\frac{144}{4}-\frac{25}{4}}$$

Since \frac{144}{4} and \frac{25}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{144-25}{4}}$$

Subtract 25 from 144 to get 119.

$$\sqrt{\frac{119}{4}}$$

Rewrite the square root of the division \sqrt{\frac{119}{4}} as the division of square roots \frac{\sqrt{119}}{\sqrt{4}}.

$$\frac{\sqrt{119}}{\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{119}}{2}$$