Solve sqrt{3250*16/314*21}

$$\sqrt{ \frac{ 3250 \times 16 }{ 314 \times 21 } }$$

Evaluate

$$\frac{20\sqrt{214305}}{3297}\approx 2.808194603$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\sqrt{\frac{16\times 1625}{21\times 157}}$$

Multiply 16 and 1625 to get 26000.

$$\sqrt{\frac{26000}{21\times 157}}$$

Multiply 21 and 157 to get 3297.

$$\sqrt{\frac{26000}{3297}}$$

Rewrite the square root of the division \sqrt{\frac{26000}{3297}} as the division of square roots \frac{\sqrt{26000}}{\sqrt{3297}}.

$$\frac{\sqrt{26000}}{\sqrt{3297}}$$

Factor 26000=20^{2}\times 65. Rewrite the square root of the product \sqrt{20^{2}\times 65} as the product of square roots \sqrt{20^{2}}\sqrt{65}. Take the square root of 20^{2}.

$$\frac{20\sqrt{65}}{\sqrt{3297}}$$

Rationalize the denominator of \frac{20\sqrt{65}}{\sqrt{3297}} by multiplying numerator and denominator by \sqrt{3297}.

$$\frac{20\sqrt{65}\sqrt{3297}}{\left(\sqrt{3297}\right)^{2}}$$

The square of \sqrt{3297} is 3297.

$$\frac{20\sqrt{65}\sqrt{3297}}{3297}$$

To multiply \sqrt{65} and \sqrt{3297}, multiply the numbers under the square root.

$$\frac{20\sqrt{214305}}{3297}$$