Solve sqrt{(15/4)^2+5^2}

$$\sqrt { ( \frac { 15 } { 4 } ) ^ { 2 } + 5 ^ { 2 } }$$

Evaluate

$$\frac{25}{4}=6.25$$

Solution Steps

Calculate \frac{15}{4} to the power of 2 and get \frac{225}{16}.

$$\sqrt{\frac{225}{16}+5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{225}{16}+25}$$

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

$$\sqrt{\frac{225}{16}+\frac{400}{16}}$$

Since \frac{225}{16} and \frac{400}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{225+400}{16}}$$

Add 225 and 400 to get 625.

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

Rewrite the square root of the division \frac{625}{16} as the division of square roots \frac{\sqrt{625}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{25}{4}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2}} = 6\frac{1}{4} = 6.25$$