Solve sqrt{9+81/16}

$$\sqrt{ 9+ \frac{ 81 }{ 16 } }$$

Evaluate

$$\frac{15}{4}=3.75$$

Solution Steps

Convert 9 to fraction \frac{144}{16}.

$$\sqrt{\frac{144}{16}+\frac{81}{16}}$$

Since \frac{144}{16} and \frac{81}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{144+81}{16}}$$

Add 144 and 81 to get 225.

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

Rewrite the square root of the division \frac{225}{16} as the division of square roots \frac{\sqrt{225}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{15}{4}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2}} = 3\frac{3}{4} = 3.75$$