Solve sqrt{1/0.1658}

$$\sqrt{ \frac{ 1 }{ 0.1658 } }$$

Evaluate

$$\frac{50\sqrt{1658}}{829}\approx 2.455883362$$

Solution Steps

Expand \frac{1}{0.1658} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{10000}{1658}}$$

Reduce the fraction \frac{10000}{1658} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{5000}{829}}$$

Rewrite the square root of the division \sqrt{\frac{5000}{829}} as the division of square roots \frac{\sqrt{5000}}{\sqrt{829}}.

$$\frac{\sqrt{5000}}{\sqrt{829}}$$

Factor 5000=50^{2}\times 2. Rewrite the square root of the product \sqrt{50^{2}\times 2} as the product of square roots \sqrt{50^{2}}\sqrt{2}. Take the square root of 50^{2}.

$$\frac{50\sqrt{2}}{\sqrt{829}}$$

Rationalize the denominator of \frac{50\sqrt{2}}{\sqrt{829}} by multiplying numerator and denominator by \sqrt{829}.

$$\frac{50\sqrt{2}\sqrt{829}}{\left(\sqrt{829}\right)^{2}}$$

The square of \sqrt{829} is 829.

$$\frac{50\sqrt{2}\sqrt{829}}{829}$$

To multiply \sqrt{2} and \sqrt{829}, multiply the numbers under the square root.

$$\frac{50\sqrt{1658}}{829}$$