Solve sqrt{21/3}div3sqrt{28}*(-12sqrt{11/2})

$$\sqrt { 2 \frac { 1 } { 3 } } \div 3 \sqrt { 28 } \times ( - 12 \sqrt { 1 \frac { 1 } { 2 } } )$$

Evaluate

$$-28\sqrt{2}\approx -39.597979746$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{\frac{6+1}{3}}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Add 6 and 1 to get 7.

$$\frac{\sqrt{\frac{7}{3}}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{7}}{\sqrt{3}}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{7}\sqrt{3}}{3}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{21}}{3}}{3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Express \frac{\frac{\sqrt{21}}{3}}{3} as a single fraction.

$$\frac{\sqrt{21}}{3\times 3}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Multiply 3 and 3 to get 9.

$$\frac{\sqrt{21}}{9}\sqrt{28}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

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}.

$$\frac{\sqrt{21}}{9}\times 2\sqrt{7}\left(-12\right)\sqrt{\frac{1\times 2+1}{2}}$$

Multiply 2 and -12 to get -24.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\sqrt{\frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\sqrt{\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\sqrt{\frac{3}{2}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\times \frac{\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\times \frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{21}}{9}\left(-24\right)\sqrt{7}\times \frac{\sqrt{6}}{2}$$

Express \frac{\sqrt{21}}{9}\left(-24\right) as a single fraction.

$$\frac{-\sqrt{21}\times 24}{9}\sqrt{7}\times \frac{\sqrt{6}}{2}$$

Express \frac{-\sqrt{21}\times 24}{9}\sqrt{7} as a single fraction.

$$\frac{-\sqrt{21}\times 24\sqrt{7}}{9}\times \frac{\sqrt{6}}{2}$$

Multiply \frac{-\sqrt{21}\times 24\sqrt{7}}{9} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{21}\times 24\sqrt{7}\sqrt{6}}{9\times 2}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{-4\sqrt{6}\sqrt{7}\sqrt{21}}{3}$$

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$\frac{-4\sqrt{6}\sqrt{7}\sqrt{7}\sqrt{3}}{3}$$

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

$$\frac{-4\sqrt{6}\times 7\sqrt{3}}{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{-4\sqrt{3}\sqrt{2}\times 7\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-4\times 3\times 7\sqrt{2}}{3}$$

Multiply -4 and 3 to get -12.

$$\frac{-12\times 7\sqrt{2}}{3}$$

Multiply -12 and 7 to get -84.

$$\frac{-84\sqrt{2}}{3}$$

Divide -84\sqrt{2} by 3 to get -28\sqrt{2}.

$$-28\sqrt{2}$$