Solve sqrt{1-18*18/21*17}

$$\sqrt { 1 - \frac { 18 \times 18 } { 21 \times 17 } }$$

Evaluate

$$\frac{\sqrt{1309}}{119}\approx 0.304034496$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\sqrt{1-\frac{6\times 18}{7\times 17}}$$

Multiply 6 and 18 to get 108.

$$\sqrt{1-\frac{108}{7\times 17}}$$

Multiply 7 and 17 to get 119.

$$\sqrt{1-\frac{108}{119}}$$

Convert 1 to fraction \frac{119}{119}.

$$\sqrt{\frac{119}{119}-\frac{108}{119}}$$

Since \frac{119}{119} and \frac{108}{119} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{119-108}{119}}$$

Subtract 108 from 119 to get 11.

$$\sqrt{\frac{11}{119}}$$

Rewrite the square root of the division \sqrt{\frac{11}{119}} as the division of square roots \frac{\sqrt{11}}{\sqrt{119}}.

$$\frac{\sqrt{11}}{\sqrt{119}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{119}} by multiplying numerator and denominator by \sqrt{119}.

$$\frac{\sqrt{11}\sqrt{119}}{\left(\sqrt{119}\right)^{2}}$$

The square of \sqrt{119} is 119.

$$\frac{\sqrt{11}\sqrt{119}}{119}$$

To multiply \sqrt{11} and \sqrt{119}, multiply the numbers under the square root.

$$\frac{\sqrt{1309}}{119}$$