Solve sqrt{2*5000/9.66}

$$\sqrt{ \frac{ 2 \times 5000 }{ 9.66 } }$$

Evaluate

$$\frac{500\sqrt{966}}{483}\approx 32.174472604$$

Solution Steps

Multiply 2 and 5000 to get 10000.

$$\sqrt{\frac{10000}{9.66}}$$

Expand \frac{10000}{9.66} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1000000}{966}}$$

Reduce the fraction \frac{1000000}{966} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{500000}{483}}$$

Rewrite the square root of the division \sqrt{\frac{500000}{483}} as the division of square roots \frac{\sqrt{500000}}{\sqrt{483}}.

$$\frac{\sqrt{500000}}{\sqrt{483}}$$

Factor 500000=500^{2}\times 2. Rewrite the square root of the product \sqrt{500^{2}\times 2} as the product of square roots \sqrt{500^{2}}\sqrt{2}. Take the square root of 500^{2}.

$$\frac{500\sqrt{2}}{\sqrt{483}}$$

Rationalize the denominator of \frac{500\sqrt{2}}{\sqrt{483}} by multiplying numerator and denominator by \sqrt{483}.

$$\frac{500\sqrt{2}\sqrt{483}}{\left(\sqrt{483}\right)^{2}}$$

The square of \sqrt{483} is 483.

$$\frac{500\sqrt{2}\sqrt{483}}{483}$$

To multiply \sqrt{2} and \sqrt{483}, multiply the numbers under the square root.

$$\frac{500\sqrt{966}}{483}$$