Solve sqrt{5.24/12-1}=

$$\sqrt { \frac { 5.24 } { 12 - 1 } } =$$

Evaluate

$$\frac{\sqrt{1441}}{55}\approx 0.690191014$$

Solution Steps

Subtract 1 from 12 to get 11.

$$\sqrt{\frac{5.24}{11}}$$

Expand \frac{5.24}{11} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{524}{1100}}$$

Reduce the fraction \frac{524}{1100} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{131}{275}}$$

Rewrite the square root of the division \sqrt{\frac{131}{275}} as the division of square roots \frac{\sqrt{131}}{\sqrt{275}}.

$$\frac{\sqrt{131}}{\sqrt{275}}$$

Factor 275=5^{2}\times 11. Rewrite the square root of the product \sqrt{5^{2}\times 11} as the product of square roots \sqrt{5^{2}}\sqrt{11}. Take the square root of 5^{2}.

$$\frac{\sqrt{131}}{5\sqrt{11}}$$

Rationalize the denominator of \frac{\sqrt{131}}{5\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{131}\sqrt{11}}{5\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{131}\sqrt{11}}{5\times 11}$$

To multiply \sqrt{131} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{1441}}{5\times 11}$$

Multiply 5 and 11 to get 55.

$$\frac{\sqrt{1441}}{55}$$