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

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

Evaluate

$$2\sqrt{7}\approx 5.291502622$$

Solution Steps

Express 2\times \frac{\sqrt{3}}{3} as a single fraction.

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

Express \frac{2\sqrt{3}}{3}\sqrt{21} as a single fraction.

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

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

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

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

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

Multiply 2 and 3 to get 6.

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

Divide 6\sqrt{7} by 3 to get 2\sqrt{7}.

$$2\sqrt{7}$$