Solve -4/3divsqrt{32}sqrt{6}

$$\frac{ -4 }{ 3 } \div \sqrt{ 32 } \sqrt{ 6 }$$

Evaluate

$$-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Solution Steps

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{-\frac{4}{3}}{\sqrt{32}}\sqrt{6}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{-\frac{4}{3}}{4\sqrt{2}}\sqrt{6}$$

Express \frac{-\frac{4}{3}}{4\sqrt{2}} as a single fraction.

$$\frac{-4}{3\times 4\sqrt{2}}\sqrt{6}$$

Rationalize the denominator of \frac{-4}{3\times 4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-4\sqrt{2}}{3\times 4\left(\sqrt{2}\right)^{2}}\sqrt{6}$$

The square of \sqrt{2} is 2.

$$\frac{-4\sqrt{2}}{3\times 4\times 2}\sqrt{6}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-\sqrt{2}}{2\times 3}\sqrt{6}$$

Multiply 2 and 3 to get 6.

$$\frac{-\sqrt{2}}{6}\sqrt{6}$$

Express \frac{-\sqrt{2}}{6}\sqrt{6} as a single fraction.

$$\frac{-\sqrt{2}\sqrt{6}}{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$\frac{-\sqrt{2}\sqrt{2}\sqrt{3}}{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{-2\sqrt{3}}{6}$$

Divide -2\sqrt{3} by 6 to get -\frac{1}{3}\sqrt{3}.

$$-\frac{1}{3}\sqrt{3}$$