Conjugates

[DavidW350]

I saw this explanation from a MGMAT instructor in an old forum question when searching for help on square roots in denominators. Was there a mistake or am I completely missing something, shouldn't the simplified expression be 8 - 4sqrt3? (see below for copy of explanation I found)


"To simplify 4 / (2 + sqrt(3))
you should multiply the numerator and denominator by (2 - sqrt 3) to get rid of the square root in the denominator

[4(2 - sqrt(3))] / [(2 + sqrt(3))(2 - sqrt(3))] = [4 - 4 sqrt(3)] / [4 - 3] = 4 - 4 sqrt (3)."

[RonPurewal]

You're right, of course.

In fact, even if you don't have any idea how to simplify the expression, it's clear that 4 - 4√3 is incorrect, since it's a negative value. The original expression is the quotient of two values that are both positive, so that's nonsense.

[RonPurewal]

Can you do us a favor, please, and post this in the actual thread where you saw the explanation? That way, we can correct it for future readers.
Thanks.