Solve sqrt{2*55000/9.65}

$$\sqrt{ \frac{ 2 \cdot 55000 }{ 9.65 } }$$

Evaluate

$$\frac{200\sqrt{10615}}{193}\approx 106.765929634$$

Solution Steps

Multiply 2 and 55000 to get 110000.

$$\sqrt{\frac{110000}{9.65}}$$

Expand \frac{110000}{9.65} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{11000000}{965}}$$

Reduce the fraction \frac{11000000}{965} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{2200000}{193}}$$

Rewrite the square root of the division \sqrt{\frac{2200000}{193}} as the division of square roots \frac{\sqrt{2200000}}{\sqrt{193}}.

$$\frac{\sqrt{2200000}}{\sqrt{193}}$$

Factor 2200000=200^{2}\times 55. Rewrite the square root of the product \sqrt{200^{2}\times 55} as the product of square roots \sqrt{200^{2}}\sqrt{55}. Take the square root of 200^{2}.

$$\frac{200\sqrt{55}}{\sqrt{193}}$$

Rationalize the denominator of \frac{200\sqrt{55}}{\sqrt{193}} by multiplying numerator and denominator by \sqrt{193}.

$$\frac{200\sqrt{55}\sqrt{193}}{\left(\sqrt{193}\right)^{2}}$$

The square of \sqrt{193} is 193.

$$\frac{200\sqrt{55}\sqrt{193}}{193}$$

To multiply \sqrt{55} and \sqrt{193}, multiply the numbers under the square root.

$$\frac{200\sqrt{10615}}{193}$$