Solve frac{frac{4sqrt{12}}{5sqrt[3]{-27}}}{frac{2sqrt{24}}{sqrt{8}}}

$$\frac{ \frac{ 4 \sqrt{ 12 } }{ 5 \sqrt[ 3 ]{ -27 } } }{ \frac{ 2 \sqrt{ 24 } }{ \sqrt{ 8 } } }$$

Evaluate

$$-\frac{4}{15}\approx -0.266666667$$

Solution Steps

Divide \frac{4\sqrt{12}}{5\sqrt[3]{-27}} by \frac{2\sqrt{24}}{\sqrt{8}} by multiplying \frac{4\sqrt{12}}{5\sqrt[3]{-27}} by the reciprocal of \frac{2\sqrt{24}}{\sqrt{8}}.

$$\frac{4\sqrt{12}\sqrt{8}}{5\sqrt[3]{-27}\times 2\sqrt{24}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\sqrt{8}\sqrt{12}}{5\sqrt{24}\sqrt[3]{-27}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\times 2\sqrt{2}\sqrt{12}}{5\sqrt{24}\sqrt[3]{-27}}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{2}\sqrt{12}}{5\sqrt{24}\sqrt[3]{-27}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{4\sqrt{2}\times 2\sqrt{3}}{5\sqrt{24}\sqrt[3]{-27}}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{2}\sqrt{3}}{5\sqrt{24}\sqrt[3]{-27}}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{8\sqrt{6}}{5\sqrt{24}\sqrt[3]{-27}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{8\sqrt{6}}{5\times 2\sqrt{6}\sqrt[3]{-27}}$$

Multiply 5 and 2 to get 10.

$$\frac{8\sqrt{6}}{10\sqrt{6}\sqrt[3]{-27}}$$

Calculate \sqrt[3]{-27} and get -3.

$$\frac{8\sqrt{6}}{10\sqrt{6}\left(-3\right)}$$

Multiply 10 and -3 to get -30.

$$\frac{8\sqrt{6}}{-30\sqrt{6}}$$

Cancel out 2\sqrt{6} in both numerator and denominator.

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

Fraction \frac{4}{-15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

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

Factor

$$-\frac{4}{15} = -0.26666666666666666$$