Solve sqrt{(9/4)^3}

$$\sqrt { ( \frac { 9 } { 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{27}{8}=3.375$$

Solution Steps

Calculate \frac{9}{4} to the power of 3 and get \frac{729}{64}.

$$\sqrt{\frac{729}{64}}$$

Rewrite the square root of the division \frac{729}{64} as the division of square roots \frac{\sqrt{729}}{\sqrt{64}}. Take the square root of both numerator and denominator.

$$\frac{27}{8}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {3}} = 3\frac{3}{8} = 3.375$$