Solve sqrt{-1^2+(5/4)^2}

$$\sqrt { - 1 ^ { 2 } + ( \frac { 5 } { 4 } ) ^ { 2 } }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\sqrt{-1+\left(\frac{5}{4}\right)^{2}}$$

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

$$\sqrt{-1+\frac{25}{16}}$$

Convert -1 to fraction -\frac{16}{16}.

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

Since -\frac{16}{16} and \frac{25}{16} have the same denominator, add them by adding their numerators.

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

Add -16 and 25 to get 9.

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

Rewrite the square root of the division \frac{9}{16} as the division of square roots \frac{\sqrt{9}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$