Solve 3/sqrt{frac{1{10}}}

$$\frac { 3 } { \sqrt { \frac { 1 } { 10 } } }$$

Evaluate

$$3\sqrt{10}\approx 9.486832981$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{10}} as the division of square roots \frac{\sqrt{1}}{\sqrt{10}}.

$$\frac{3}{\frac{\sqrt{1}}{\sqrt{10}}}$$

Calculate the square root of 1 and get 1.

$$\frac{3}{\frac{1}{\sqrt{10}}}$$

Rationalize the denominator of \frac{1}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3}{\frac{\sqrt{10}}{\left(\sqrt{10}\right)^{2}}}$$

The square of \sqrt{10} is 10.

$$\frac{3}{\frac{\sqrt{10}}{10}}$$

Divide 3 by \frac{\sqrt{10}}{10} by multiplying 3 by the reciprocal of \frac{\sqrt{10}}{10}.

$$\frac{3\times 10}{\sqrt{10}}$$

Rationalize the denominator of \frac{3\times 10}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\times 10\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{3\times 10\sqrt{10}}{10}$$

Multiply 3 and 10 to get 30.

$$\frac{30\sqrt{10}}{10}$$

Divide 30\sqrt{10} by 10 to get 3\sqrt{10}.

$$3\sqrt{10}$$