Solve sqrt{379/90}

$$\sqrt { \frac { 379 } { 90 } }$$

Evaluate

$$\frac{\sqrt{3790}}{30}\approx 2.052099196$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{379}{90}} as the division of square roots \frac{\sqrt{379}}{\sqrt{90}}.

$$\frac{\sqrt{379}}{\sqrt{90}}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{\sqrt{379}}{3\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{379}}{3\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{379}\sqrt{10}}{3\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{379}\sqrt{10}}{3\times 10}$$

To multiply \sqrt{379} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{3790}}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$\frac{\sqrt{3790}}{30}$$