Solve frac{2sqrt{5}}{sqrt{2}}:sqrt{10/994}=

$$\frac { 2 \sqrt { 5 } } { \sqrt { 2 } } : \sqrt { \frac { 10 } { 994 } } =$$

Evaluate

$$\sqrt{994}\approx 31.527765541$$

Solution Steps

Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{2\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{\sqrt{\frac{10}{994}}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{2\sqrt{5}\sqrt{2}}{2}}{\sqrt{\frac{10}{994}}}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\frac{2\sqrt{10}}{2}}{\sqrt{\frac{10}{994}}}$$

Cancel out 2 and 2.

$$\frac{\sqrt{10}}{\sqrt{\frac{10}{994}}}$$

Reduce the fraction \frac{10}{994} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{10}}{\sqrt{\frac{5}{497}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{497}} as the division of square roots \frac{\sqrt{5}}{\sqrt{497}}.

$$\frac{\sqrt{10}}{\frac{\sqrt{5}}{\sqrt{497}}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{497}} by multiplying numerator and denominator by \sqrt{497}.

$$\frac{\sqrt{10}}{\frac{\sqrt{5}\sqrt{497}}{\left(\sqrt{497}\right)^{2}}}$$

The square of \sqrt{497} is 497.

$$\frac{\sqrt{10}}{\frac{\sqrt{5}\sqrt{497}}{497}}$$

To multiply \sqrt{5} and \sqrt{497}, multiply the numbers under the square root.

$$\frac{\sqrt{10}}{\frac{\sqrt{2485}}{497}}$$

Divide \sqrt{10} by \frac{\sqrt{2485}}{497} by multiplying \sqrt{10} by the reciprocal of \frac{\sqrt{2485}}{497}.

$$\frac{\sqrt{10}\times 497}{\sqrt{2485}}$$

Rationalize the denominator of \frac{\sqrt{10}\times 497}{\sqrt{2485}} by multiplying numerator and denominator by \sqrt{2485}.

$$\frac{\sqrt{10}\times 497\sqrt{2485}}{\left(\sqrt{2485}\right)^{2}}$$

The square of \sqrt{2485} is 2485.

$$\frac{\sqrt{10}\times 497\sqrt{2485}}{2485}$$

To multiply \sqrt{10} and \sqrt{2485}, multiply the numbers under the square root.

$$\frac{\sqrt{24850}\times 497}{2485}$$

Factor 24850=5^{2}\times 994. Rewrite the square root of the product \sqrt{5^{2}\times 994} as the product of square roots \sqrt{5^{2}}\sqrt{994}. Take the square root of 5^{2}.

$$\frac{5\sqrt{994}\times 497}{2485}$$

Multiply 5 and 497 to get 2485.

$$\frac{2485\sqrt{994}}{2485}$$

Cancel out 2485 and 2485.

$$\sqrt{994}$$