Solve sqrt{4.8div6}*241

$$\sqrt{ 4.8 \div 6 } \times 241$$

Evaluate

$$\frac{482\sqrt{5}}{5}\approx 215.556953031$$

Solution Steps

Expand \frac{4.8}{6} by multiplying both numerator and the denominator by 10.

$$241\sqrt{\frac{48}{60}}$$

Reduce the fraction \frac{48}{60} to lowest terms by extracting and canceling out 12.

$$241\sqrt{\frac{4}{5}}$$

Rewrite the square root of the division \sqrt{\frac{4}{5}} as the division of square roots \frac{\sqrt{4}}{\sqrt{5}}.

$$241\times \frac{\sqrt{4}}{\sqrt{5}}$$

Calculate the square root of 4 and get 2.

$$241\times \frac{2}{\sqrt{5}}$$

Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$241\times \frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$241\times \frac{2\sqrt{5}}{5}$$

Express 241\times \frac{2\sqrt{5}}{5} as a single fraction.

$$\frac{241\times 2\sqrt{5}}{5}$$

Multiply 241 and 2 to get 482.

$$\frac{482\sqrt{5}}{5}$$