Solve -sqrt{27}div(3/10)sqrt{3/8}

$$- \sqrt { 27 } \div ( \frac { 3 } { 10 } ) \sqrt { \frac { 3 } { 8 } }$$

Evaluate

$$-\frac{15\sqrt{2}}{2}\approx -10.606601718$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\sqrt{\frac{3}{8}}$$

Rewrite the square root of the division \sqrt{\frac{3}{8}} as the division of square roots \frac{\sqrt{3}}{\sqrt{8}}.

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{3}}{\sqrt{8}}$$

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}.

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{3}}{2\sqrt{2}}$$

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

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}$$

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

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{-3\sqrt{3}}{\frac{3}{10}}\times \frac{\sqrt{6}}{4}$$

Divide -3\sqrt{3} by \frac{3}{10} by multiplying -3\sqrt{3} by the reciprocal of \frac{3}{10}.

$$\frac{\left(-3\sqrt{3}\right)\times 10}{3}\times \frac{\sqrt{6}}{4}$$

Multiply \frac{\left(-3\sqrt{3}\right)\times 10}{3} times \frac{\sqrt{6}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-3\sqrt{3}\right)\times 10\sqrt{6}}{3\times 4}$$

Cancel out 2 in both numerator and denominator.

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

Multiply 5 and -1 to get -5.

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

Multiply -5 and 3 to get -15.

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

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}.

$$\frac{-15\sqrt{3}\sqrt{3}\sqrt{2}}{2\times 3}$$

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

$$\frac{-15\times 3\sqrt{2}}{2\times 3}$$

Multiply 2 and 3 to get 6.

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

Multiply -15 and 3 to get -45.

$$\frac{-45\sqrt{2}}{6}$$

Divide -45\sqrt{2} by 6 to get -\frac{15}{2}\sqrt{2}.

$$-\frac{15}{2}\sqrt{2}$$