Solve sqrt{24^2+{left(5/12right)}^2}

$$\sqrt{ { 24 }^{ 2 } + { \left( \frac{ 5 }{ 12 } \right) }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{82969}}{12}\approx 24.003616626$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\sqrt{576+\left(\frac{5}{12}\right)^{2}}$$

Calculate \frac{5}{12} to the power of 2 and get \frac{25}{144}.

$$\sqrt{576+\frac{25}{144}}$$

Convert 576 to fraction \frac{82944}{144}.

$$\sqrt{\frac{82944}{144}+\frac{25}{144}}$$

Since \frac{82944}{144} and \frac{25}{144} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{82944+25}{144}}$$

Add 82944 and 25 to get 82969.

$$\sqrt{\frac{82969}{144}}$$

Rewrite the square root of the division \sqrt{\frac{82969}{144}} as the division of square roots \frac{\sqrt{82969}}{\sqrt{144}}.

$$\frac{\sqrt{82969}}{\sqrt{144}}$$

Calculate the square root of 144 and get 12.

$$\frac{\sqrt{82969}}{12}$$