Solve -4/3sqrt{18}div2sqrt{8}*1/3sqrt{54}

$$- \frac{ 4 }{ 3 } \sqrt{ 18 } \div 2 \sqrt{ 8 } \times \frac{ 1 }{ 3 } \sqrt{ 54 }$$

Evaluate

$$-8\sqrt{6}\approx -19.595917942$$

Solution Steps

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}.

$$\frac{-\frac{4}{3}\times 3\sqrt{2}}{2}\sqrt{8}\times \frac{1}{3}\sqrt{54}$$

Cancel out 3 and 3.

$$\frac{-4\sqrt{2}}{2}\sqrt{8}\times \frac{1}{3}\sqrt{54}$$

Divide -4\sqrt{2} by 2 to get -2\sqrt{2}.

$$-2\sqrt{2}\sqrt{8}\times \frac{1}{3}\sqrt{54}$$

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}.

$$-2\sqrt{2}\times 2\sqrt{2}\times \frac{1}{3}\sqrt{54}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{2}\sqrt{2}\times \frac{1}{3}\sqrt{54}$$

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

$$-4\times 2\times \frac{1}{3}\sqrt{54}$$

Multiply -4 and \frac{1}{3} to get \frac{-4}{3}.

$$\frac{-4}{3}\times 2\sqrt{54}$$

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

$$-\frac{4}{3}\times 2\sqrt{54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

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

Cancel out 3 and 3.

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

Multiply -4 and 2 to get -8.

$$-8\sqrt{6}$$