Solve sqrt{74div84}

$$\sqrt{ 74 \div 84 }$$

Evaluate

$$\frac{\sqrt{1554}}{42}\approx 0.938590635$$

Solution Steps

Reduce the fraction \frac{74}{84} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{37}{42}}$$

Rewrite the square root of the division \sqrt{\frac{37}{42}} as the division of square roots \frac{\sqrt{37}}{\sqrt{42}}.

$$\frac{\sqrt{37}}{\sqrt{42}}$$

Rationalize the denominator of \frac{\sqrt{37}}{\sqrt{42}} by multiplying numerator and denominator by \sqrt{42}.

$$\frac{\sqrt{37}\sqrt{42}}{\left(\sqrt{42}\right)^{2}}$$

The square of \sqrt{42} is 42.

$$\frac{\sqrt{37}\sqrt{42}}{42}$$

To multiply \sqrt{37} and \sqrt{42}, multiply the numbers under the square root.

$$\frac{\sqrt{1554}}{42}$$