Solve sqrt{1/0.2290}

$$\sqrt{ \frac{ 1 }{ 0.2290 } }$$

Evaluate

$$\frac{10\sqrt{2290}}{229}\approx 2.089691898$$

Solution Steps

Expand \frac{1}{0.229} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1000}{229}}$$

Rewrite the square root of the division \sqrt{\frac{1000}{229}} as the division of square roots \frac{\sqrt{1000}}{\sqrt{229}}.

$$\frac{\sqrt{1000}}{\sqrt{229}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{10\sqrt{10}}{\sqrt{229}}$$

Rationalize the denominator of \frac{10\sqrt{10}}{\sqrt{229}} by multiplying numerator and denominator by \sqrt{229}.

$$\frac{10\sqrt{10}\sqrt{229}}{\left(\sqrt{229}\right)^{2}}$$

The square of \sqrt{229} is 229.

$$\frac{10\sqrt{10}\sqrt{229}}{229}$$

To multiply \sqrt{10} and \sqrt{229}, multiply the numbers under the square root.

$$\frac{10\sqrt{2290}}{229}$$