# Thread: Rationalize the denominator and simplify - help

1. ## Rationalize 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??

2. Originally Posted by mcruz65
√(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??

$\sqrt{40}=\sqrt{4}\sqrt{10}=2\sqrt{10}$

Tonio

3. Originally Posted by mcruz65
√(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 $\frac{9}{\sqrt{40}}$

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

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

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

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