Solve frac{-2sqrt{21}sqrt{72}}{sqrt{60}}

$$\frac{ -2 \sqrt{ 21 } \sqrt{ 72 } }{ \sqrt{ 60 } }$$

Evaluate

$$-\frac{6\sqrt{70}}{5}\approx -10.039920318$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{-2\sqrt{21}\times 6\sqrt{2}}{\sqrt{60}}$$

Multiply -2 and 6 to get -12.

$$\frac{-12\sqrt{21}\sqrt{2}}{\sqrt{60}}$$

To multiply \sqrt{21} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{-12\sqrt{42}}{\sqrt{60}}$$

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}.

$$\frac{-12\sqrt{42}}{2\sqrt{15}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-6\sqrt{42}}{\sqrt{15}}$$

Rationalize the denominator of \frac{-6\sqrt{42}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{-6\sqrt{42}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{-6\sqrt{42}\sqrt{15}}{15}$$

To multiply \sqrt{42} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{-6\sqrt{630}}{15}$$

Factor 630=3^{2}\times 70. Rewrite the square root of the product \sqrt{3^{2}\times 70} as the product of square roots \sqrt{3^{2}}\sqrt{70}. Take the square root of 3^{2}.

$$\frac{-6\times 3\sqrt{70}}{15}$$

Multiply -6 and 3 to get -18.

$$\frac{-18\sqrt{70}}{15}$$

Divide -18\sqrt{70} by 15 to get -\frac{6}{5}\sqrt{70}.

$$-\frac{6}{5}\sqrt{70}$$