Solve sqrt{2*3000*1000/0.35*1000}

$$\sqrt{ \frac{ 2 \times 3000 \times 1000 }{ 0.35 \times 1000 } }$$

Evaluate

$$\frac{200\sqrt{21}}{7}\approx 130.930734142$$

Solution Steps

Cancel out 2\times 500 in both numerator and denominator.

$$\sqrt{\frac{6\times 1000}{0.35}}$$

Multiply 6 and 1000 to get 6000.

$$\sqrt{\frac{6000}{0.35}}$$

Expand \frac{6000}{0.35} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{600000}{35}}$$

Reduce the fraction \frac{600000}{35} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{120000}{7}}$$

Rewrite the square root of the division \sqrt{\frac{120000}{7}} as the division of square roots \frac{\sqrt{120000}}{\sqrt{7}}.

$$\frac{\sqrt{120000}}{\sqrt{7}}$$

Factor 120000=200^{2}\times 3. Rewrite the square root of the product \sqrt{200^{2}\times 3} as the product of square roots \sqrt{200^{2}}\sqrt{3}. Take the square root of 200^{2}.

$$\frac{200\sqrt{3}}{\sqrt{7}}$$

Rationalize the denominator of \frac{200\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{200\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{200\sqrt{3}\sqrt{7}}{7}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{200\sqrt{21}}{7}$$