Solve 3sqrt{9861/8000}

$$3 \sqrt{ \frac{ 9861 }{ 8000 } }$$

Evaluate

$$\frac{3\sqrt{49305}}{200}\approx 3.330709384$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{9861}{8000}} as the division of square roots \frac{\sqrt{9861}}{\sqrt{8000}}.

$$3\times \frac{\sqrt{9861}}{\sqrt{8000}}$$

Factor 8000=40^{2}\times 5. Rewrite the square root of the product \sqrt{40^{2}\times 5} as the product of square roots \sqrt{40^{2}}\sqrt{5}. Take the square root of 40^{2}.

$$3\times \frac{\sqrt{9861}}{40\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{9861}}{40\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$3\times \frac{\sqrt{9861}\sqrt{5}}{40\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$3\times \frac{\sqrt{9861}\sqrt{5}}{40\times 5}$$

To multiply \sqrt{9861} and \sqrt{5}, multiply the numbers under the square root.

$$3\times \frac{\sqrt{49305}}{40\times 5}$$

Multiply 40 and 5 to get 200.

$$3\times \frac{\sqrt{49305}}{200}$$

Express 3\times \frac{\sqrt{49305}}{200} as a single fraction.

$$\frac{3\sqrt{49305}}{200}$$