Solve sqrt{2*10000/9.78}

$$\sqrt{ \frac{ 2 \cdot 10000 }{ 9.78 } }$$

Evaluate

$$\frac{1000\sqrt{489}}{489}\approx 45.221563165$$

Solution Steps

Multiply 2 and 10000 to get 20000.

$$\sqrt{\frac{20000}{9.78}}$$

Expand \frac{20000}{9.78} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{2000000}{978}}$$

Reduce the fraction \frac{2000000}{978} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1000000}{489}}$$

Rewrite the square root of the division \sqrt{\frac{1000000}{489}} as the division of square roots \frac{\sqrt{1000000}}{\sqrt{489}}.

$$\frac{\sqrt{1000000}}{\sqrt{489}}$$

Calculate the square root of 1000000 and get 1000.

$$\frac{1000}{\sqrt{489}}$$

Rationalize the denominator of \frac{1000}{\sqrt{489}} by multiplying numerator and denominator by \sqrt{489}.

$$\frac{1000\sqrt{489}}{\left(\sqrt{489}\right)^{2}}$$

The square of \sqrt{489} is 489.

$$\frac{1000\sqrt{489}}{489}$$