Solve 1/2sqrt{14}*2/7sqrt{21}

$$\frac { 1 } { 2 } \sqrt { 14 } * \frac { 2 } { 7 } \sqrt { 21 }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Multiply \frac{1}{2} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{2\times 7}\sqrt{14}\sqrt{21}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{7}\sqrt{14}\sqrt{21}$$

To multiply \sqrt{14} and \sqrt{21}, multiply the numbers under the square root.

$$\frac{1}{7}\sqrt{294}$$

Factor 294=7^{2}\times 6. Rewrite the square root of the product \sqrt{7^{2}\times 6} as the product of square roots \sqrt{7^{2}}\sqrt{6}. Take the square root of 7^{2}.

$$\frac{1}{7}\times 7\sqrt{6}$$

Cancel out 7 and 7.

$$\sqrt{6}$$