Solve sqrt{86/144}

$$\sqrt { \frac { 86 } { 144 } }$$

Evaluate

$$\frac{\sqrt{86}}{12}\approx 0.772801541$$

Solution Steps

Reduce the fraction \frac{86}{144} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{43}{72}}$$

Rewrite the square root of the division \sqrt{\frac{43}{72}} as the division of square roots \frac{\sqrt{43}}{\sqrt{72}}.

$$\frac{\sqrt{43}}{\sqrt{72}}$$

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}.

$$\frac{\sqrt{43}}{6\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{43}}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{43}\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{43}\sqrt{2}}{6\times 2}$$

To multiply \sqrt{43} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{86}}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$\frac{\sqrt{86}}{12}$$