Solve sqrt{45div6}*241

$$\sqrt{ 45 \div 6 } \times 241$$

Evaluate

$$\frac{241\sqrt{30}}{2}\approx 660.005681794$$

Solution Steps

Reduce the fraction \frac{45}{6} to lowest terms by extracting and canceling out 3.

$$241\sqrt{\frac{15}{2}}$$

Rewrite the square root of the division \sqrt{\frac{15}{2}} as the division of square roots \frac{\sqrt{15}}{\sqrt{2}}.

$$241\times \frac{\sqrt{15}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{15}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$241\times \frac{\sqrt{15}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$241\times \frac{\sqrt{15}\sqrt{2}}{2}$$

To multiply \sqrt{15} and \sqrt{2}, multiply the numbers under the square root.

$$241\times \frac{\sqrt{30}}{2}$$

Express 241\times \frac{\sqrt{30}}{2} as a single fraction.

$$\frac{241\sqrt{30}}{2}$$