Solve sqrt{2*20000/9.75}

$$\sqrt{ \frac{ 2 \cdot 20000 }{ 9.75 } }$$

Evaluate

$$\frac{400\sqrt{39}}{39}\approx 64.051261522$$

Solution Steps

Multiply 2 and 20000 to get 40000.

$$\sqrt{\frac{40000}{9.75}}$$

Expand \frac{40000}{9.75} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{4000000}{975}}$$

Reduce the fraction \frac{4000000}{975} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{160000}{39}}$$

Rewrite the square root of the division \sqrt{\frac{160000}{39}} as the division of square roots \frac{\sqrt{160000}}{\sqrt{39}}.

$$\frac{\sqrt{160000}}{\sqrt{39}}$$

Calculate the square root of 160000 and get 400.

$$\frac{400}{\sqrt{39}}$$

Rationalize the denominator of \frac{400}{\sqrt{39}} by multiplying numerator and denominator by \sqrt{39}.

$$\frac{400\sqrt{39}}{\left(\sqrt{39}\right)^{2}}$$

The square of \sqrt{39} is 39.

$$\frac{400\sqrt{39}}{39}$$