Solve sqrt{1.581div4}

$$\sqrt{ 1.581 \div 4 }$$

Evaluate

$$\frac{\sqrt{15810}}{200}\approx 0.628689112$$

Solution Steps

Expand \frac{1.581}{4} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1581}{4000}}$$

Rewrite the square root of the division \sqrt{\frac{1581}{4000}} as the division of square roots \frac{\sqrt{1581}}{\sqrt{4000}}.

$$\frac{\sqrt{1581}}{\sqrt{4000}}$$

Factor 4000=20^{2}\times 10. Rewrite the square root of the product \sqrt{20^{2}\times 10} as the product of square roots \sqrt{20^{2}}\sqrt{10}. Take the square root of 20^{2}.

$$\frac{\sqrt{1581}}{20\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{1581}}{20\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{1581}\sqrt{10}}{20\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{1581}\sqrt{10}}{20\times 10}$$

To multiply \sqrt{1581} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{15810}}{20\times 10}$$

Multiply 20 and 10 to get 200.

$$\frac{\sqrt{15810}}{200}$$