Solve sqrt{{left(10/3right)}^2+{left(5/2right)}^2}

$$\sqrt{ { \left( \frac{ 10 }{ 3 } \right) }^{ 2 } + { \left( \frac{ 5 }{ 2 } \right) }^{ 2 } }$$

Evaluate

$$\frac{25}{6}\approx 4.166666667$$

Solution Steps

Calculate \frac{10}{3} to the power of 2 and get \frac{100}{9}.

$$\sqrt{\frac{100}{9}+\left(\frac{5}{2}\right)^{2}}$$

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

$$\sqrt{\frac{100}{9}+\frac{25}{4}}$$

Least common multiple of 9 and 4 is 36. Convert \frac{100}{9} and \frac{25}{4} to fractions with denominator 36.

$$\sqrt{\frac{400}{36}+\frac{225}{36}}$$

Since \frac{400}{36} and \frac{225}{36} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{400+225}{36}}$$

Add 400 and 225 to get 625.

$$\sqrt{\frac{625}{36}}$$

Rewrite the square root of the division \frac{625}{36} as the division of square roots \frac{\sqrt{625}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{25}{6}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$$