Solve sqrt{5.2div6}*241

$$\sqrt{ 5.2 \div 6 } \times 241$$

Evaluate

$$\frac{241\sqrt{195}}{15}\approx 224.358790037$$

Solution Steps

Expand \frac{5.2}{6} by multiplying both numerator and the denominator by 10.

$$241\sqrt{\frac{52}{60}}$$

Reduce the fraction \frac{52}{60} to lowest terms by extracting and canceling out 4.

$$241\sqrt{\frac{13}{15}}$$

Rewrite the square root of the division \sqrt{\frac{13}{15}} as the division of square roots \frac{\sqrt{13}}{\sqrt{15}}.

$$241\times \frac{\sqrt{13}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{13}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$241\times \frac{\sqrt{13}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$241\times \frac{\sqrt{13}\sqrt{15}}{15}$$

To multiply \sqrt{13} and \sqrt{15}, multiply the numbers under the square root.

$$241\times \frac{\sqrt{195}}{15}$$

Express 241\times \frac{\sqrt{195}}{15} as a single fraction.

$$\frac{241\sqrt{195}}{15}$$