Solve sqrt{21/2}div2sqrt{28}*(-sqrt{22/7})

$$\sqrt { 2 \frac { 1 } { 2 } } \div 2 \sqrt { 28 } \times ( - \sqrt { 2 \frac { 2 } { 7 } } )$$

Evaluate

$$-2\sqrt{10}\approx -6.32455532$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{\frac{4+1}{2}}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

Add 4 and 1 to get 5.

$$\frac{\sqrt{\frac{5}{2}}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

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

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

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

$$\frac{\frac{\sqrt{10}}{2}}{2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

Express \frac{\frac{\sqrt{10}}{2}}{2} as a single fraction.

$$\frac{\sqrt{10}}{2\times 2}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{10}}{4}\sqrt{28}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\sqrt{\frac{2\times 7+2}{7}}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\sqrt{\frac{14+2}{7}}\right)$$

Add 14 and 2 to get 16.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\sqrt{\frac{16}{7}}\right)$$

Rewrite the square root of the division \sqrt{\frac{16}{7}} as the division of square roots \frac{\sqrt{16}}{\sqrt{7}}.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\frac{\sqrt{16}}{\sqrt{7}}\right)$$

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\frac{4}{\sqrt{7}}\right)$$

Rationalize the denominator of \frac{4}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\frac{4\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\right)$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{10}}{4}\times 2\sqrt{7}\left(-\frac{4\sqrt{7}}{7}\right)$$

Cancel out 4, the greatest common factor in 2 and 4.

$$\frac{\sqrt{10}}{2}\sqrt{7}\left(-\frac{4\sqrt{7}}{7}\right)$$

Express \frac{\sqrt{10}}{2}\sqrt{7} as a single fraction.

$$\frac{\sqrt{10}\sqrt{7}}{2}\left(-\frac{4\sqrt{7}}{7}\right)$$

Multiply \frac{\sqrt{10}\sqrt{7}}{2} times -\frac{4\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{10}\sqrt{7}\times 4\sqrt{7}}{2\times 7}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-2\sqrt{7}\sqrt{7}\sqrt{10}}{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{-2\times 7\sqrt{10}}{7}$$

Cancel out 7 and 7.

$$-2\sqrt{10}$$