Solve frac{sqrt{2.7}*sqrt{33}}{sqrt{1.1}}

$$\frac { \sqrt { 2.7 } \times \sqrt { 33 } } { \sqrt { 1.1 } }$$

Evaluate

$$9$$

Solution Steps

To multiply \sqrt{2.7} and \sqrt{33}, multiply the numbers under the square root.

$$\frac{\sqrt{89.1}}{\sqrt{1.1}}$$

Rationalize the denominator of \frac{\sqrt{89.1}}{\sqrt{1.1}} by multiplying numerator and denominator by \sqrt{1.1}.

$$\frac{\sqrt{89.1}\sqrt{1.1}}{\left(\sqrt{1.1}\right)^{2}}$$

The square of \sqrt{1.1} is 1.1.

$$\frac{\sqrt{89.1}\sqrt{1.1}}{1.1}$$

To multiply \sqrt{89.1} and \sqrt{1.1}, multiply the numbers under the square root.

$$\frac{\sqrt{98.01}}{1.1}$$

Calculate the square root of 98.01 and get 9.9.

$$\frac{9.9}{1.1}$$

Expand \frac{9.9}{1.1} by multiplying both numerator and the denominator by 10.

$$\frac{99}{11}$$

Divide 99 by 11 to get 9.

$$9$$

Factor

$$3^{2}$$