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

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

Evaluate

$$\frac{\sqrt{481}}{20}\approx 1.09658561$$

Solution Steps

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

$$\sqrt{\frac{9}{16}+\left(-\frac{4}{5}\right)^{2}}$$

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

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

Least common multiple of 16 and 25 is 400. Convert \frac{9}{16} and \frac{16}{25} to fractions with denominator 400.

$$\sqrt{\frac{225}{400}+\frac{256}{400}}$$

Since \frac{225}{400} and \frac{256}{400} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{225+256}{400}}$$

Add 225 and 256 to get 481.

$$\sqrt{\frac{481}{400}}$$

Rewrite the square root of the division \sqrt{\frac{481}{400}} as the division of square roots \frac{\sqrt{481}}{\sqrt{400}}.

$$\frac{\sqrt{481}}{\sqrt{400}}$$

Calculate the square root of 400 and get 20.

$$\frac{\sqrt{481}}{20}$$