Solve sqrt{6^2+(7/4)^2}

$$\sqrt { 6 ^ { 2 } + ( \frac { 7 } { 4 } ) ^ { 2 } }$$

Evaluate

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

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36+\left(\frac{7}{4}\right)^{2}}$$

Calculate \frac{7}{4} to the power of 2 and get \frac{49}{16}.

$$\sqrt{36+\frac{49}{16}}$$

Convert 36 to fraction \frac{576}{16}.

$$\sqrt{\frac{576}{16}+\frac{49}{16}}$$

Since \frac{576}{16} and \frac{49}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{576+49}{16}}$$

Add 576 and 49 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

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