√(81/40)

√81/√40=9/√40

In order to rationalize the denominator, I begin by factoring the denominator 40.

40 = 2 x 2 x 2 x 5

I am not getting anywhere with this line of logic. What am I doing wrong??

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- Mar 14th 2010, 07:02 PMmcruz65Rationalize the denominator and simplify - help
√(81/40)

√81/√40=9/√40

In order to rationalize the denominator, I begin by factoring the denominator 40.

40 = 2 x 2 x 2 x 5

I am not getting anywhere with this line of logic. What am I doing wrong?? - Mar 14th 2010, 07:30 PMtonio
- Mar 14th 2010, 07:36 PMmasters
Hi mcruz65,

You have it down to $\displaystyle \frac{9}{\sqrt{40}}$

Let's think of the largest perfect square factor of 40. That would be 4 because 4 times 10 is 40. So, rewrite

$\displaystyle \frac{9}{\sqrt{40}}=\frac{9}{\sqrt{4\cdot10}}=\fra c{9}{2\sqrt{10}}$

Now, to rationalize the denominator, we must multiply both numerator and denominator by $\displaystyle \sqrt{10}$.

$\displaystyle \frac{9}{2\sqrt{10}}\cdot \frac{\sqrt{10}}{\sqrt{10}}=\frac{9\sqrt{10}}{20}$