Solve sqrt{8000/867}

$$\sqrt{ \frac{ 8000 }{ 867 } }$$

Evaluate

$$\frac{40\sqrt{15}}{51}\approx 3.037633997$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8000}{867}} as the division of square roots \frac{\sqrt{8000}}{\sqrt{867}}.

$$\frac{\sqrt{8000}}{\sqrt{867}}$$

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}.

$$\frac{40\sqrt{5}}{\sqrt{867}}$$

Factor 867=17^{2}\times 3. Rewrite the square root of the product \sqrt{17^{2}\times 3} as the product of square roots \sqrt{17^{2}}\sqrt{3}. Take the square root of 17^{2}.

$$\frac{40\sqrt{5}}{17\sqrt{3}}$$

Rationalize the denominator of \frac{40\sqrt{5}}{17\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{40\sqrt{5}\sqrt{3}}{17\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{40\sqrt{5}\sqrt{3}}{17\times 3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{40\sqrt{15}}{17\times 3}$$

Multiply 17 and 3 to get 51.

$$\frac{40\sqrt{15}}{51}$$