Solve -sqrt{44/5}*sqrt{21/2}

$$- \sqrt{ 4 \frac{ 4 }{ 5 } } \times \sqrt{ 2 \frac{ 1 }{ 2 } }$$

Evaluate

$$-2\sqrt{3}\approx -3.464101615$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\left(-\sqrt{\frac{20+4}{5}}\right)\sqrt{\frac{2\times 2+1}{2}}$$

Add 20 and 4 to get 24.

$$\left(-\sqrt{\frac{24}{5}}\right)\sqrt{\frac{2\times 2+1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{24}{5}} as the division of square roots \frac{\sqrt{24}}{\sqrt{5}}.

$$\left(-\frac{\sqrt{24}}{\sqrt{5}}\right)\sqrt{\frac{2\times 2+1}{2}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{2\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

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

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$\left(-\frac{2\sqrt{30}}{5}\right)\sqrt{\frac{2\times 2+1}{2}}$$

Multiply 2 and 2 to get 4.

$$\left(-\frac{2\sqrt{30}}{5}\right)\sqrt{\frac{4+1}{2}}$$

Add 4 and 1 to get 5.

$$\left(-\frac{2\sqrt{30}}{5}\right)\sqrt{\frac{5}{2}}$$

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\left(-\frac{2\sqrt{30}}{5}\right)\times \frac{\sqrt{5}}{\sqrt{2}}$$

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

$$\left(-\frac{2\sqrt{30}}{5}\right)\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\left(-\frac{2\sqrt{30}}{5}\right)\times \frac{\sqrt{5}\sqrt{2}}{2}$$

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

$$\left(-\frac{2\sqrt{30}}{5}\right)\times \frac{\sqrt{10}}{2}$$

Multiply -\frac{2\sqrt{30}}{5} times \frac{\sqrt{10}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\sqrt{30}\sqrt{10}}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\sqrt{10}\sqrt{30}}{5}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$\frac{-\sqrt{10}\sqrt{10}\sqrt{3}}{5}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{-10\sqrt{3}}{5}$$

Divide -10\sqrt{3} by 5 to get -2\sqrt{3}.

$$-2\sqrt{3}$$