√(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??
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 $\displaystyle \sqrt{10}$.
$\displaystyle \frac{9}{2\sqrt{10}}\cdot \frac{\sqrt{10}}{\sqrt{10}}=\frac{9\sqrt{10}}{20}$