Solve sqrt{12/2.523}

$$\sqrt { \frac { 12 } { 2.523 } }$$

Evaluate

$$\frac{20\sqrt{10}}{29}\approx 2.180881145$$

Solution Steps

Expand \frac{12}{2.523} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{12000}{2523}}$$

Reduce the fraction \frac{12000}{2523} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{4000}{841}}$$

Rewrite the square root of the division \sqrt{\frac{4000}{841}} as the division of square roots \frac{\sqrt{4000}}{\sqrt{841}}.

$$\frac{\sqrt{4000}}{\sqrt{841}}$$

Factor 4000=20^{2}\times 10. Rewrite the square root of the product \sqrt{20^{2}\times 10} as the product of square roots \sqrt{20^{2}}\sqrt{10}. Take the square root of 20^{2}.

$$\frac{20\sqrt{10}}{\sqrt{841}}$$

Calculate the square root of 841 and get 29.

$$\frac{20\sqrt{10}}{29}$$