Solve sqrt{(25/4)^2-4}

$$\sqrt { ( \frac { 25 } { 4 } ) ^ { 2 } - 4 }$$

Evaluate

$$\frac{\sqrt{561}}{4}\approx 5.921359641$$

Solution Steps

Calculate \frac{25}{4} to the power of 2 and get \frac{625}{16}.

$$\sqrt{\frac{625}{16}-4}$$

Convert 4 to fraction \frac{64}{16}.

$$\sqrt{\frac{625}{16}-\frac{64}{16}}$$

Since \frac{625}{16} and \frac{64}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{625-64}{16}}$$

Subtract 64 from 625 to get 561.

$$\sqrt{\frac{561}{16}}$$

Rewrite the square root of the division \sqrt{\frac{561}{16}} as the division of square roots \frac{\sqrt{561}}{\sqrt{16}}.

$$\frac{\sqrt{561}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{561}}{4}$$