Solve sqrt{4.7div6}*241

$$\sqrt{ 4.7 \div 6 } \times 241$$

Evaluate

$$\frac{241\sqrt{705}}{30}\approx 213.299749961$$

Solution Steps

Expand \frac{4.7}{6} by multiplying both numerator and the denominator by 10.

$$241\sqrt{\frac{47}{60}}$$

Rewrite the square root of the division \sqrt{\frac{47}{60}} as the division of square roots \frac{\sqrt{47}}{\sqrt{60}}.

$$241\times \frac{\sqrt{47}}{\sqrt{60}}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$241\times \frac{\sqrt{47}}{2\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{47}}{2\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$241\times \frac{\sqrt{47}\sqrt{15}}{2\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$241\times \frac{\sqrt{47}\sqrt{15}}{2\times 15}$$

To multiply \sqrt{47} and \sqrt{15}, multiply the numbers under the square root.

$$241\times \frac{\sqrt{705}}{2\times 15}$$

Multiply 2 and 15 to get 30.

$$241\times \frac{\sqrt{705}}{30}$$

Express 241\times \frac{\sqrt{705}}{30} as a single fraction.

$$\frac{241\sqrt{705}}{30}$$