Solve sqrt{87/12-(1/12)^2*10}

$$\sqrt { \frac { 87 } { 12 } - ( 1 / 12 ) ^ { 2 } \times 10 }$$

Evaluate

$$\frac{\sqrt{1034}}{12}\approx 2.679655865$$

Solution Steps

Reduce the fraction \frac{87}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{29}{4}-\left(\frac{1}{12}\right)^{2}\times 10}$$

Calculate \frac{1}{12} to the power of 2 and get \frac{1}{144}.

$$\sqrt{\frac{29}{4}-\frac{1}{144}\times 10}$$

Multiply \frac{1}{144} and 10 to get \frac{10}{144}.

$$\sqrt{\frac{29}{4}-\frac{10}{144}}$$

Reduce the fraction \frac{10}{144} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{29}{4}-\frac{5}{72}}$$

Least common multiple of 4 and 72 is 72. Convert \frac{29}{4} and \frac{5}{72} to fractions with denominator 72.

$$\sqrt{\frac{522}{72}-\frac{5}{72}}$$

Since \frac{522}{72} and \frac{5}{72} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{522-5}{72}}$$

Subtract 5 from 522 to get 517.

$$\sqrt{\frac{517}{72}}$$

Rewrite the square root of the division \sqrt{\frac{517}{72}} as the division of square roots \frac{\sqrt{517}}{\sqrt{72}}.

$$\frac{\sqrt{517}}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{\sqrt{517}}{6\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{517}}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{517}\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{517}\sqrt{2}}{6\times 2}$$

To multiply \sqrt{517} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{1034}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\sqrt{1034}}{12}$$