Solve sqrt{21/2}div3sqrt{2}sqrt{8}*(-sqrt{127})

$$\sqrt { 2 \frac { 1 } { 2 } } \div 3 \sqrt { 2 } \sqrt { 8 } \times ( - \sqrt { 127 } )$$

Evaluate

$$-\frac{2\sqrt{1270}}{3}\approx -23.758039575$$

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$\frac{\sqrt{\frac{2\times 2+1}{2}}}{3}\sqrt{2}\sqrt{2}\sqrt{4}\left(-\sqrt{127}\right)$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{\sqrt{\frac{2\times 2+1}{2}}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{\frac{4+1}{2}}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

Add 4 and 1 to get 5.

$$\frac{\sqrt{\frac{5}{2}}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

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

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

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

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

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

$$\frac{\frac{\sqrt{10}}{2}}{3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

Express \frac{\frac{\sqrt{10}}{2}}{3} as a single fraction.

$$\frac{\sqrt{10}}{2\times 3}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{10}}{6}\times 2\sqrt{4}\left(-\sqrt{127}\right)$$

Calculate the square root of 4 and get 2.

$$\frac{\sqrt{10}}{6}\times 2\times 2\left(-\sqrt{127}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{10}}{6}\times 4\left(-\sqrt{127}\right)$$

Express \frac{\sqrt{10}}{6}\times 4 as a single fraction.

$$\frac{\sqrt{10}\times 4}{6}\left(-\sqrt{127}\right)$$

Express \frac{\sqrt{10}\times 4}{6}\left(-\sqrt{127}\right) as a single fraction.

$$\frac{-\sqrt{10}\times 4\sqrt{127}}{6}$$

Multiply -1 and 4 to get -4.

$$\frac{-4\sqrt{10}\sqrt{127}}{6}$$

To multiply \sqrt{10} and \sqrt{127}, multiply the numbers under the square root.

$$\frac{-4\sqrt{1270}}{6}$$

Divide -4\sqrt{1270} by 6 to get -\frac{2}{3}\sqrt{1270}.

$$-\frac{2}{3}\sqrt{1270}$$