Solve sqrt{2*25000/9.74}

$$\sqrt{ \frac{ 2 \cdot 25000 }{ 9.74 } }$$

Evaluate

$$\frac{500\sqrt{4870}}{487}\approx 71.648239517$$

Solution Steps

Multiply 2 and 25000 to get 50000.

$$\sqrt{\frac{50000}{9.74}}$$

Expand \frac{50000}{9.74} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{5000000}{974}}$$

Reduce the fraction \frac{5000000}{974} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{2500000}{487}}$$

Rewrite the square root of the division \sqrt{\frac{2500000}{487}} as the division of square roots \frac{\sqrt{2500000}}{\sqrt{487}}.

$$\frac{\sqrt{2500000}}{\sqrt{487}}$$

Factor 2500000=500^{2}\times 10. Rewrite the square root of the product \sqrt{500^{2}\times 10} as the product of square roots \sqrt{500^{2}}\sqrt{10}. Take the square root of 500^{2}.

$$\frac{500\sqrt{10}}{\sqrt{487}}$$

Rationalize the denominator of \frac{500\sqrt{10}}{\sqrt{487}} by multiplying numerator and denominator by \sqrt{487}.

$$\frac{500\sqrt{10}\sqrt{487}}{\left(\sqrt{487}\right)^{2}}$$

The square of \sqrt{487} is 487.

$$\frac{500\sqrt{10}\sqrt{487}}{487}$$

To multiply \sqrt{10} and \sqrt{487}, multiply the numbers under the square root.

$$\frac{500\sqrt{4870}}{487}$$