Solve 2sqrt{6}*sqrt{1/2}quadsqrt{28}8*sqrt{1/12}

$$2 \sqrt { 6 } \times \sqrt { \frac { 1 } { 2 } } \quad \sqrt { 28 } 8 \times \sqrt { \frac { 1 } { 12 } }$$

Evaluate

$$16\sqrt{7}\approx 42.332020977$$

Solution Steps

To multiply \sqrt{\frac{1}{2}} and \sqrt{\frac{1}{12}}, multiply the numbers under the square root.

$$2\times 8\sqrt{6}\sqrt{\frac{1}{24}}\sqrt{28}$$

Multiply 2 and 8 to get 16.

$$16\sqrt{6}\sqrt{\frac{1}{24}}\sqrt{28}$$

Rewrite the square root of the division \sqrt{\frac{1}{24}} as the division of square roots \frac{\sqrt{1}}{\sqrt{24}}.

$$16\sqrt{6}\times \frac{\sqrt{1}}{\sqrt{24}}\sqrt{28}$$

Calculate the square root of 1 and get 1.

$$16\sqrt{6}\times \frac{1}{\sqrt{24}}\sqrt{28}$$

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}.

$$16\sqrt{6}\times \frac{1}{2\sqrt{6}}\sqrt{28}$$

Rationalize the denominator of \frac{1}{2\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$16\sqrt{6}\times \frac{\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}\sqrt{28}$$

The square of \sqrt{6} is 6.

$$16\sqrt{6}\times \frac{\sqrt{6}}{2\times 6}\sqrt{28}$$

Multiply 2 and 6 to get 12.

$$16\sqrt{6}\times \frac{\sqrt{6}}{12}\sqrt{28}$$

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}.

$$16\sqrt{6}\times \frac{\sqrt{6}}{12}\times 2\sqrt{7}$$

Multiply 16 and 2 to get 32.

$$32\sqrt{6}\times \frac{\sqrt{6}}{12}\sqrt{7}$$

Express 32\times \frac{\sqrt{6}}{12} as a single fraction.

$$\frac{32\sqrt{6}}{12}\sqrt{6}\sqrt{7}$$

Express \frac{32\sqrt{6}}{12}\sqrt{7} as a single fraction.

$$\frac{32\sqrt{6}\sqrt{7}}{12}\sqrt{6}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{32\sqrt{42}}{12}\sqrt{6}$$

Divide 32\sqrt{42} by 12 to get \frac{8}{3}\sqrt{42}.

$$\frac{8}{3}\sqrt{42}\sqrt{6}$$

Factor 42=6\times 7. Rewrite the square root of the product \sqrt{6\times 7} as the product of square roots \sqrt{6}\sqrt{7}.

$$\frac{8}{3}\sqrt{6}\sqrt{7}\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{8}{3}\times 6\sqrt{7}$$

Express \frac{8}{3}\times 6 as a single fraction.

$$\frac{8\times 6}{3}\sqrt{7}$$

Multiply 8 and 6 to get 48.

$$\frac{48}{3}\sqrt{7}$$

Divide 48 by 3 to get 16.

$$16\sqrt{7}$$