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

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

Evaluate

$$\frac{5\sqrt{3}}{2}\approx 4.330127019$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25-\left(\frac{5}{2}\right)^{2}}$$

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

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

Convert 25 to fraction \frac{100}{4}.

$$\sqrt{\frac{100}{4}-\frac{25}{4}}$$

Since \frac{100}{4} and \frac{25}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{100-25}{4}}$$

Subtract 25 from 100 to get 75.

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

Rewrite the square root of the division \sqrt{\frac{75}{4}} as the division of square roots \frac{\sqrt{75}}{\sqrt{4}}.

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

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

Calculate the square root of 4 and get 2.

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