Solve frac{sqrt{21}}{3}*frac{3sqrt{6}}{2}

$$\frac{ \sqrt{ 21 } }{ 3 } \times \frac{ 3 \sqrt{ 6 } }{ 2 }$$

Evaluate

$$\frac{3\sqrt{14}}{2}\approx 5.61248608$$

Solution Steps

Multiply \frac{\sqrt{21}}{3} times \frac{3\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{21}\times 3\sqrt{6}}{3\times 2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{6}\sqrt{21}}{2}$$

To multiply \sqrt{6} and \sqrt{21}, multiply the numbers under the square root.

$$\frac{\sqrt{126}}{2}$$

Factor 126=3^{2}\times 14. Rewrite the square root of the product \sqrt{3^{2}\times 14} as the product of square roots \sqrt{3^{2}}\sqrt{14}. Take the square root of 3^{2}.

$$\frac{3\sqrt{14}}{2}$$