Solve -frac{3sqrt{3}}{9sqrt{21}}

$$- \frac { 3 \sqrt { 3 } } { 9 \sqrt { 21 } }$$

Evaluate

$$-\frac{\sqrt{7}}{21}\approx -0.125988158$$

Solution Steps

Cancel out 3 in both numerator and denominator.

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

Rationalize the denominator of \frac{\sqrt{3}}{3\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

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

The square of \sqrt{21} is 21.

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

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}.

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

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

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

Multiply 3 and 21 to get 63.

$$-\frac{3\sqrt{7}}{63}$$

Divide 3\sqrt{7} by 63 to get \frac{1}{21}\sqrt{7}.

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