Solve sqrt{15}*3/5sqrt{20}div(-1/3sqrt{6})

$$\sqrt { 15 } \times \frac { 3 } { 5 } \sqrt { 20 } \div ( - \frac { 1 } { 3 } \sqrt { 6 } )$$

Evaluate

$$-9\sqrt{2}\approx -12.727922061$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{\sqrt{15}\times \frac{3}{5}\times 2\sqrt{5}}{-\frac{1}{3}\sqrt{6}}$$

Express \frac{3}{5}\times 2 as a single fraction.

$$\frac{\sqrt{15}\times \frac{3\times 2}{5}\sqrt{5}}{-\frac{1}{3}\sqrt{6}}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{15}\times \frac{6}{5}\sqrt{5}}{-\frac{1}{3}\sqrt{6}}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{\sqrt{5}\sqrt{3}\times \frac{6}{5}\sqrt{5}}{-\frac{1}{3}\sqrt{6}}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\times \frac{6}{5}\sqrt{3}}{-\frac{1}{3}\sqrt{6}}$$

Rationalize the denominator of \frac{5\times \frac{6}{5}\sqrt{3}}{-\frac{1}{3}\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{5\times \frac{6}{5}\sqrt{3}\sqrt{6}}{-\frac{1}{3}\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{5\times \frac{6}{5}\sqrt{3}\sqrt{6}}{-\frac{1}{3}\times 6}$$

Cancel out 5 and 5.

$$\frac{6\sqrt{3}\sqrt{6}}{-\frac{1}{3}\times 6}$$

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

$$\frac{6\sqrt{3}\sqrt{3}\sqrt{2}}{-\frac{1}{3}\times 6}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{6\times 3\sqrt{2}}{-\frac{1}{3}\times 6}$$

Express -\frac{1}{3}\times 6 as a single fraction.

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

Divide -6 by 3 to get -2.

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

Multiply 6 and 3 to get 18.

$$\frac{18\sqrt{2}}{-2}$$

Divide 18\sqrt{2} by -2 to get -9\sqrt{2}.

$$-9\sqrt{2}$$