Solve (-9)^3/sqrt{27}

$$\frac { ( - 9 ) ^ { 3 } } { \sqrt { 27 } }$$

Evaluate

$$-81\sqrt{3}\approx -140.296115413$$

Solution Steps

Calculate -9 to the power of 3 and get -729.

$$\frac{-729}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{-729}{3\sqrt{3}}$$

Rationalize the denominator of \frac{-729}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-729\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{-729\sqrt{3}}{3\times 3}$$

Cancel out 3\times 3 in both numerator and denominator.

$$-81\sqrt{3}$$