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

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

Evaluate

$$\frac{5\sqrt{10}}{3}\approx 5.270462767$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25+\left(\frac{5}{3}\right)^{2}}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

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

Convert 25 to fraction \frac{225}{9}.

$$\sqrt{\frac{225}{9}+\frac{25}{9}}$$

Since \frac{225}{9} and \frac{25}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{225+25}{9}}$$

Add 225 and 25 to get 250.

$$\sqrt{\frac{250}{9}}$$

Rewrite the square root of the division \sqrt{\frac{250}{9}} as the division of square roots \frac{\sqrt{250}}{\sqrt{9}}.

$$\frac{\sqrt{250}}{\sqrt{9}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{5\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{5\sqrt{10}}{3}$$