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

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

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

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

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

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

$$\sqrt{\frac{25}{16}+\frac{4}{9}}$$

Least common multiple of 16 and 9 is 144. Convert \frac{25}{16} and \frac{4}{9} to fractions with denominator 144.

$$\sqrt{\frac{225}{144}+\frac{64}{144}}$$

Since \frac{225}{144} and \frac{64}{144} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{225+64}{144}}$$

Add 225 and 64 to get 289.

$$\sqrt{\frac{289}{144}}$$

Rewrite the square root of the division \frac{289}{144} as the division of square roots \frac{\sqrt{289}}{\sqrt{144}}. Take the square root of both numerator and denominator.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$