Solve frac{(-3)^2-4sqrt{18}}{(-8)^frac{2{3}}}

$$\frac { ( - 3 ) ^ { 2 } - 4 \sqrt { 18 } } { ( - 8 ) ^ { \frac { 2 } { 3 } } }$$

Evaluate

$$\frac{9}{4}-3\sqrt{2}\approx -1.992640687$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\frac{9-4\sqrt{18}}{\left(-8\right)^{\frac{2}{3}}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{9-4\times 3\sqrt{2}}{\left(-8\right)^{\frac{2}{3}}}$$

Multiply -4 and 3 to get -12.

$$\frac{9-12\sqrt{2}}{\left(-8\right)^{\frac{2}{3}}}$$

Calculate -8 to the power of \frac{2}{3} and get 4.

$$\frac{9-12\sqrt{2}}{4}$$