Determine whether its ture or false. when rationalizing the denominator of (14)/(4-√3), you multiply by √3/√3

Answer 1

The answer is no. When you have an expression in the denominator, such as 4-√3. you multiply by the conjugate over the conjugate, (4+√3) / (4+√3). Let's try them both out:

(14)/(4-√3) x (√3/√3) = 14√3 / (4√3-3)

So I still have a √3 in the denominator. Let's try the conjugate:

(14)/(4-√3) x (4+√3)/(4+√3) = ((64+14√3) / 7

So we have successfully gotten the square root out of the denominator!

Answer 2

To "rationalize the denominator" means to make the denominator a rational number, i.e. no square roots. So if multiplying by √3/√3 gets rid of all square roots in the denominator, then it's rationalized. Let's try it:

14 × √3 14√3 14√3

———————— —— = ———————————— = —————————————

(4 - √3) × √3 4√3 - √3√3 4√3 - 3

We can no longer simplify, and as we can see, there's still a square root in the denominator, so it is not rationalized. Therefore, the answer to your question is false.

So if we can't rationalize the denominator by multiplying by √3/√3, how might we be able to rationalize it? Think about it if you'd like :)