Solve sqrt{1/4*11/10}

$$\sqrt { \frac { 1 } { 4 } \cdot \frac { 11 } { 10 } }$$

Evaluate

$$\frac{\sqrt{110}}{20}\approx 0.524404424$$

Solution Steps

Multiply \frac{1}{4} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{1\times 11}{4\times 10}}$$

Do the multiplications in the fraction \frac{1\times 11}{4\times 10}.

$$\sqrt{\frac{11}{40}}$$

Rewrite the square root of the division \sqrt{\frac{11}{40}} as the division of square roots \frac{\sqrt{11}}{\sqrt{40}}.

$$\frac{\sqrt{11}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{\sqrt{11}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{11}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{11}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{11}\sqrt{10}}{2\times 10}$$

To multiply \sqrt{11} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{110}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{\sqrt{110}}{20}$$