Solve sqrt{3.5div6}*241

$$\sqrt{ 3.5 \div 6 } \times 241$$

Evaluate

$$\frac{241\sqrt{21}}{6}\approx 184.066790414$$

Solution Steps

Expand \frac{3.5}{6} by multiplying both numerator and the denominator by 10.

$$241\sqrt{\frac{35}{60}}$$

Reduce the fraction \frac{35}{60} to lowest terms by extracting and canceling out 5.

$$241\sqrt{\frac{7}{12}}$$

Rewrite the square root of the division \sqrt{\frac{7}{12}} as the division of square roots \frac{\sqrt{7}}{\sqrt{12}}.

$$241\times \frac{\sqrt{7}}{\sqrt{12}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$241\times \frac{\sqrt{7}}{2\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{7}}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$241\times \frac{\sqrt{7}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$241\times \frac{\sqrt{7}\sqrt{3}}{2\times 3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$241\times \frac{\sqrt{21}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$241\times \frac{\sqrt{21}}{6}$$

Express 241\times \frac{\sqrt{21}}{6} as a single fraction.

$$\frac{241\sqrt{21}}{6}$$