Solve sqrt{{left(25/4right)}^2+5^2}

$$\sqrt{ { \left( \frac{ 25 }{ 4 } \right) }^{ 2 } + { 5 }^{ 2 } }$$

Evaluate

$$\frac{5\sqrt{41}}{4}\approx 8.003905297$$

Solution Steps

Calculate \frac{25}{4} to the power of 2 and get \frac{625}{16}.

$$\sqrt{\frac{625}{16}+5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{625}{16}+25}$$

Convert 25 to fraction \frac{400}{16}.

$$\sqrt{\frac{625}{16}+\frac{400}{16}}$$

Since \frac{625}{16} and \frac{400}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{625+400}{16}}$$

Add 625 and 400 to get 1025.

$$\sqrt{\frac{1025}{16}}$$

Rewrite the square root of the division \sqrt{\frac{1025}{16}} as the division of square roots \frac{\sqrt{1025}}{\sqrt{16}}.

$$\frac{\sqrt{1025}}{\sqrt{16}}$$

Factor 1025=5^{2}\times 41. Rewrite the square root of the product \sqrt{5^{2}\times 41} as the product of square roots \sqrt{5^{2}}\sqrt{41}. Take the square root of 5^{2}.

$$\frac{5\sqrt{41}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{5\sqrt{41}}{4}$$