Solve 1/2*frac{sqrt{3}}{2}*1/sqrt{21}

$$\frac { 1 } { 2 } \times \frac { \sqrt { 3 } } { 2 } \times \frac { 1 } { \sqrt { 21 } }$$

Evaluate

$$\frac{\sqrt{7}}{28}\approx 0.094491118$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{1}{2}\times \frac{\sqrt{3}}{2}\times \frac{\sqrt{21}}{\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$\frac{1}{2}\times \frac{\sqrt{3}}{2}\times \frac{\sqrt{21}}{21}$$

Multiply \frac{1}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{7}}{2\times 2\times 21}$$

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

$$\frac{3\sqrt{7}}{2\times 2\times 21}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{7}}{4\times 21}$$

Multiply 4 and 21 to get 84.

$$\frac{3\sqrt{7}}{84}$$

Divide 3\sqrt{7} by 84 to get \frac{1}{28}\sqrt{7}.

$$\frac{1}{28}\sqrt{7}$$