Solve sqrt{2*70000/9.60}

$$\sqrt{ \frac{ 2 \times 70000 }{ 9.60 } }$$

Evaluate

$$\frac{25\sqrt{210}}{3}\approx 120.761472885$$

Solution Steps

Multiply 2 and 70000 to get 140000.

$$\sqrt{\frac{140000}{9.6}}$$

Expand \frac{140000}{9.6} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1400000}{96}}$$

Reduce the fraction \frac{1400000}{96} to lowest terms by extracting and canceling out 32.

$$\sqrt{\frac{43750}{3}}$$

Rewrite the square root of the division \sqrt{\frac{43750}{3}} as the division of square roots \frac{\sqrt{43750}}{\sqrt{3}}.

$$\frac{\sqrt{43750}}{\sqrt{3}}$$

Factor 43750=25^{2}\times 70. Rewrite the square root of the product \sqrt{25^{2}\times 70} as the product of square roots \sqrt{25^{2}}\sqrt{70}. Take the square root of 25^{2}.

$$\frac{25\sqrt{70}}{\sqrt{3}}$$

Rationalize the denominator of \frac{25\sqrt{70}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{25\sqrt{70}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{25\sqrt{70}\sqrt{3}}{3}$$

To multiply \sqrt{70} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{25\sqrt{210}}{3}$$