Solve sqrt{1000div29}

$$\sqrt{ 1000 \div 29 }$$

Evaluate

$$\frac{10\sqrt{290}}{29}\approx 5.872202195$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1000}{29}} as the division of square roots \frac{\sqrt{1000}}{\sqrt{29}}.

$$\frac{\sqrt{1000}}{\sqrt{29}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

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

Rationalize the denominator of \frac{10\sqrt{10}}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{10\sqrt{10}\sqrt{29}}{\left(\sqrt{29}\right)^{2}}$$

The square of \sqrt{29} is 29.

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

To multiply \sqrt{10} and \sqrt{29}, multiply the numbers under the square root.

$$\frac{10\sqrt{290}}{29}$$