Solve sqrt{(5/4)^2-(3/4)^2}

$$\sqrt { ( \frac { 5 } { 4 } ) ^ { 2 } - ( \frac { 3 } { 4 } ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\sqrt{\frac{25}{16}-\left(\frac{3}{4}\right)^{2}}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\sqrt{\frac{25}{16}-\frac{9}{16}}$$

Since \frac{25}{16} and \frac{9}{16} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{25-9}{16}}$$

Subtract 9 from 25 to get 16.

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

Divide 16 by 16 to get 1.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$