Solve 6sqrt{6}*(-12sqrt{5/8})

$$6 \sqrt { 6 } \times ( - 12 \sqrt { \frac { 5 } { 8 } } )$$

Evaluate

$$-36\sqrt{15}\approx -139.427400463$$

Solution Steps

Multiply 6 and -12 to get -72.

$$-72\sqrt{6}\sqrt{\frac{5}{8}}$$

Rewrite the square root of the division \sqrt{\frac{5}{8}} as the division of square roots \frac{\sqrt{5}}{\sqrt{8}}.

$$-72\sqrt{6}\times \frac{\sqrt{5}}{\sqrt{8}}$$

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}.

$$-72\sqrt{6}\times \frac{\sqrt{5}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-72\sqrt{6}\times \frac{\sqrt{5}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-72\sqrt{6}\times \frac{\sqrt{5}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$-72\sqrt{6}\times \frac{\sqrt{10}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$-72\sqrt{6}\times \frac{\sqrt{10}}{4}$$

Cancel out 4, the greatest common factor in 72 and 4.

$$-18\sqrt{10}\sqrt{6}$$

To multiply \sqrt{10} and \sqrt{6}, multiply the numbers under the square root.

$$-18\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$-18\times 2\sqrt{15}$$

Multiply -18 and 2 to get -36.

$$-36\sqrt{15}$$