Solve sqrt{(-25/6+3)^2+16}

$$\sqrt { ( - \frac { 25 } { 6 } + 3 ) ^ { 2 } + 16 }$$

Evaluate

$$\frac{25}{6}\approx 4.166666667$$

Solution Steps

Add -\frac{25}{6} and 3 to get -\frac{7}{6}.

$$\sqrt{\left(-\frac{7}{6}\right)^{2}+16}$$

Calculate -\frac{7}{6} to the power of 2 and get \frac{49}{36}.

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

Add \frac{49}{36} and 16 to get \frac{625}{36}.

$$\sqrt{\frac{625}{36}}$$

Rewrite the square root of the division \frac{625}{36} as the division of square roots \frac{\sqrt{625}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$\frac{25}{6}$$

Factor

$$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$$