Solve sqrt{{left(-5/8right)}^2}+{left(7/8right)}^2

$$\sqrt{ { \left(- \frac{ 5 }{ 8 } \right) }^{ 2 } } + { \left( \frac{ 7 }{ 8 } \right) }^{ 2 }$$

Evaluate

$$\frac{89}{64}=1.390625$$

Solution Steps

Calculate -\frac{5}{8} to the power of 2 and get \frac{25}{64}.

$$\sqrt{\frac{25}{64}}+\left(\frac{7}{8}\right)^{2}$$

Rewrite the square root of the division \frac{25}{64} as the division of square roots \frac{\sqrt{25}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$\frac{5}{8}+\left(\frac{7}{8}\right)^{2}$$

Calculate \frac{7}{8} to the power of 2 and get \frac{49}{64}.

$$\frac{5}{8}+\frac{49}{64}$$

Least common multiple of 8 and 64 is 64. Convert \frac{5}{8} and \frac{49}{64} to fractions with denominator 64.

$$\frac{40}{64}+\frac{49}{64}$$

Since \frac{40}{64} and \frac{49}{64} have the same denominator, add them by adding their numerators.

$$\frac{40+49}{64}$$

Add 40 and 49 to get 89.

$$\frac{89}{64}$$

Factor

$$\frac{89}{2 ^ {6}} = 1\frac{25}{64} = 1.390625$$