Solve sqrt{2*10*25.5*3.8/293}

$$\sqrt{ \frac{ 2 \cdot 10 \cdot 25.5 \cdot 3.8 }{ 293 } }$$

Evaluate

$$\frac{\sqrt{567834}}{293}\approx 2.571834845$$

Solution Steps

Multiply 2 and 10 to get 20.

$$\sqrt{\frac{20\times 25.5\times 3.8}{293}}$$

Multiply 20 and 25.5 to get 510.

$$\sqrt{\frac{510\times 3.8}{293}}$$

Multiply 510 and 3.8 to get 1938.

$$\sqrt{\frac{1938}{293}}$$

Rewrite the square root of the division \sqrt{\frac{1938}{293}} as the division of square roots \frac{\sqrt{1938}}{\sqrt{293}}.

$$\frac{\sqrt{1938}}{\sqrt{293}}$$

Rationalize the denominator of \frac{\sqrt{1938}}{\sqrt{293}} by multiplying numerator and denominator by \sqrt{293}.

$$\frac{\sqrt{1938}\sqrt{293}}{\left(\sqrt{293}\right)^{2}}$$

The square of \sqrt{293} is 293.

$$\frac{\sqrt{1938}\sqrt{293}}{293}$$

To multiply \sqrt{1938} and \sqrt{293}, multiply the numbers under the square root.

$$\frac{\sqrt{567834}}{293}$$