Solve frac{11sqrt{20+31}}{12sqrt{20+51}}

$$\frac { 11 \sqrt { 20 + 31 } } { 12 \sqrt { 20 + 51 } }$$

Evaluate

$$\frac{11\sqrt{3621}}{852}\approx 0.776903992$$

Solution Steps

Add 20 and 31 to get 51.

$$\frac{11\sqrt{51}}{12\sqrt{20+51}}$$

Add 20 and 51 to get 71.

$$\frac{11\sqrt{51}}{12\sqrt{71}}$$

Rationalize the denominator of \frac{11\sqrt{51}}{12\sqrt{71}} by multiplying numerator and denominator by \sqrt{71}.

$$\frac{11\sqrt{51}\sqrt{71}}{12\left(\sqrt{71}\right)^{2}}$$

The square of \sqrt{71} is 71.

$$\frac{11\sqrt{51}\sqrt{71}}{12\times 71}$$

To multiply \sqrt{51} and \sqrt{71}, multiply the numbers under the square root.

$$\frac{11\sqrt{3621}}{12\times 71}$$

Multiply 12 and 71 to get 852.

$$\frac{11\sqrt{3621}}{852}$$