Solve sqrt{0.1446/(13-2)}=

$$\sqrt { 0.1446 / ( 13 - 2 ) } =$$

Evaluate

$$\frac{\sqrt{15906}}{1100}\approx 0.114653629$$

Solution Steps

Subtract 2 from 13 to get 11.

$$\sqrt{\frac{0.1446}{11}}$$

Expand \frac{0.1446}{11} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{1446}{110000}}$$

Reduce the fraction \frac{1446}{110000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{723}{55000}}$$

Rewrite the square root of the division \sqrt{\frac{723}{55000}} as the division of square roots \frac{\sqrt{723}}{\sqrt{55000}}.

$$\frac{\sqrt{723}}{\sqrt{55000}}$$

Factor 55000=50^{2}\times 22. Rewrite the square root of the product \sqrt{50^{2}\times 22} as the product of square roots \sqrt{50^{2}}\sqrt{22}. Take the square root of 50^{2}.

$$\frac{\sqrt{723}}{50\sqrt{22}}$$

Rationalize the denominator of \frac{\sqrt{723}}{50\sqrt{22}} by multiplying numerator and denominator by \sqrt{22}.

$$\frac{\sqrt{723}\sqrt{22}}{50\left(\sqrt{22}\right)^{2}}$$

The square of \sqrt{22} is 22.

$$\frac{\sqrt{723}\sqrt{22}}{50\times 22}$$

To multiply \sqrt{723} and \sqrt{22}, multiply the numbers under the square root.

$$\frac{\sqrt{15906}}{50\times 22}$$

Multiply 50 and 22 to get 1100.

$$\frac{\sqrt{15906}}{1100}$$