Solve sqrt{8.1396/16-1}=

$$\sqrt { \frac { 8.1396 } { 16 - 1 } } =$$

Evaluate

$$\frac{\sqrt{33915}}{250}\approx 0.736641025$$

Solution Steps

Subtract 1 from 16 to get 15.

$$\sqrt{\frac{8.1396}{15}}$$

Expand \frac{8.1396}{15} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{81396}{150000}}$$

Reduce the fraction \frac{81396}{150000} to lowest terms by extracting and canceling out 12.

$$\sqrt{\frac{6783}{12500}}$$

Rewrite the square root of the division \sqrt{\frac{6783}{12500}} as the division of square roots \frac{\sqrt{6783}}{\sqrt{12500}}.

$$\frac{\sqrt{6783}}{\sqrt{12500}}$$

Factor 12500=50^{2}\times 5. Rewrite the square root of the product \sqrt{50^{2}\times 5} as the product of square roots \sqrt{50^{2}}\sqrt{5}. Take the square root of 50^{2}.

$$\frac{\sqrt{6783}}{50\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{6783}}{50\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{6783}\sqrt{5}}{50\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{6783}\sqrt{5}}{50\times 5}$$

To multiply \sqrt{6783} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{33915}}{50\times 5}$$

Multiply 50 and 5 to get 250.

$$\frac{\sqrt{33915}}{250}$$