Solve frac{sqrt{66}*sqrt{65}}{sqrt{165}*sqrt{104}}*frac{sqrt{165}*sqrt{104}}{sqrt{165}*sqrt{104}}

$$\frac{ \sqrt{ 66 } \times \sqrt{ 65 } }{ \sqrt{ 165 } \times \sqrt{ 104 } } \times \frac{ \sqrt{ 165 } \times \sqrt{ 104 } }{ \sqrt{ 165 } \times \sqrt{ 104 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Divide \sqrt{165}\sqrt{104} by \sqrt{165}\sqrt{104} to get 1.

$$\frac{\sqrt{66}\sqrt{65}}{\sqrt{165}\sqrt{104}}\times 1$$

To multiply \sqrt{66} and \sqrt{65}, multiply the numbers under the square root.

$$\frac{\sqrt{4290}}{\sqrt{165}\sqrt{104}}\times 1$$

Factor 104=2^{2}\times 26. Rewrite the square root of the product \sqrt{2^{2}\times 26} as the product of square roots \sqrt{2^{2}}\sqrt{26}. Take the square root of 2^{2}.

$$\frac{\sqrt{4290}}{\sqrt{165}\times 2\sqrt{26}}\times 1$$

To multiply \sqrt{165} and \sqrt{26}, multiply the numbers under the square root.

$$\frac{\sqrt{4290}}{\sqrt{4290}\times 2}\times 1$$

Rationalize the denominator of \frac{\sqrt{4290}}{\sqrt{4290}\times 2} by multiplying numerator and denominator by \sqrt{4290}.

$$\frac{\sqrt{4290}\sqrt{4290}}{\left(\sqrt{4290}\right)^{2}\times 2}\times 1$$

The square of \sqrt{4290} is 4290.

$$\frac{\sqrt{4290}\sqrt{4290}}{4290\times 2}\times 1$$

Multiply \sqrt{4290} and \sqrt{4290} to get 4290.

$$\frac{4290}{4290\times 2}\times 1$$

Multiply 4290 and 2 to get 8580.

$$\frac{4290}{8580}\times 1$$

Reduce the fraction \frac{4290}{8580} to lowest terms by extracting and canceling out 4290.

$$\frac{1}{2}\times 1$$

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$