Solve -sqrt{frac{1/4}}{sqrt{16/21}}

$$- \frac { \sqrt { \frac { 1 } { 4 } } } { \sqrt { \frac { 16 } { 21 } } }$$

Evaluate

$$-\frac{\sqrt{21}}{8}\approx -0.572821962$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-\frac{\frac{1}{2}}{\sqrt{\frac{16}{21}}}$$

Rewrite the square root of the division \sqrt{\frac{16}{21}} as the division of square roots \frac{\sqrt{16}}{\sqrt{21}}.

$$-\frac{\frac{1}{2}}{\frac{\sqrt{16}}{\sqrt{21}}}$$

Calculate the square root of 16 and get 4.

$$-\frac{\frac{1}{2}}{\frac{4}{\sqrt{21}}}$$

Rationalize the denominator of \frac{4}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$-\frac{\frac{1}{2}}{\frac{4\sqrt{21}}{\left(\sqrt{21}\right)^{2}}}$$

The square of \sqrt{21} is 21.

$$-\frac{\frac{1}{2}}{\frac{4\sqrt{21}}{21}}$$

Divide \frac{1}{2} by \frac{4\sqrt{21}}{21} by multiplying \frac{1}{2} by the reciprocal of \frac{4\sqrt{21}}{21}.

$$-\frac{21}{2\times 4\sqrt{21}}$$

Rationalize the denominator of \frac{21}{2\times 4\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$-\frac{21\sqrt{21}}{2\times 4\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$-\frac{21\sqrt{21}}{2\times 4\times 21}$$

Cancel out 21 in both numerator and denominator.

$$-\frac{\sqrt{21}}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$-\frac{\sqrt{21}}{8}$$