Solve 2sqrt{12}*frac{sqrt{7}}{4}

$$2 \sqrt { 12 } \times \frac { \sqrt { 7 } } { 4 }$$

Evaluate

$$\sqrt{21}\approx 4.582575695$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

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

Cancel out 4 and 4.

$$\sqrt{7}\sqrt{3}$$

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

$$\sqrt{21}$$