Solve frac{2sqrt{7}}{7}*frac{sqrt{21}}{7}*2

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

Evaluate

$$\frac{4\sqrt{3}}{7}\approx 0.989743319$$

Solution Steps

Express 2\times \frac{2\sqrt{7}}{7} as a single fraction.

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

Multiply \frac{2\times 2\sqrt{7}}{7} times \frac{\sqrt{21}}{7} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply \sqrt{7} and \sqrt{7} to get 7.

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

Multiply 2 and 2 to get 4.

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

Multiply 4 and 7 to get 28.

$$\frac{28\sqrt{3}}{7\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{28\sqrt{3}}{49}$$

Divide 28\sqrt{3} by 49 to get \frac{4}{7}\sqrt{3}.

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