Solve sqrt{2*31/2.17}

$$\sqrt { \frac { 2 \times 31 } { 2.17 } }$$

Evaluate

$$\frac{10\sqrt{14}}{7}\approx 5.345224838$$

Solution Steps

Multiply 2 and 31 to get 62.

$$\sqrt{\frac{62}{2.17}}$$

Expand \frac{62}{2.17} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{6200}{217}}$$

Reduce the fraction \frac{6200}{217} to lowest terms by extracting and canceling out 31.

$$\sqrt{\frac{200}{7}}$$

Rewrite the square root of the division \sqrt{\frac{200}{7}} as the division of square roots \frac{\sqrt{200}}{\sqrt{7}}.

$$\frac{\sqrt{200}}{\sqrt{7}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{10\sqrt{2}}{\sqrt{7}}$$

Rationalize the denominator of \frac{10\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{10\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{10\sqrt{2}\sqrt{7}}{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{10\sqrt{14}}{7}$$