SOLUTION: My son asked me tonight this question: What is the Reciprocal of the sqrt(3) My mind is boggled and I don't know how to answer or even where to begin to figure it out. HELP??

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: My son asked me tonight this question: What is the Reciprocal of the sqrt(3) My mind is boggled and I don't know how to answer or even where to begin to figure it out. HELP??       Log On

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Question 94747: My son asked me tonight this question: What is the Reciprocal of the sqrt(3)
My mind is boggled and I don't know how to answer or even where to begin to figure it out. HELP??
Answer by bucky(2100) About Me  (Show Source):
You can put this solution on YOUR website!
The reciprocal means "1 divided by ..." So the reciprocal of the square root of 3 means:
.
1%2Fsqrt%283%29
.
But convention is that you do not leave a radical (in this case sqrt%283%29) in the denominator.
The way you get rid of the square root of 3 is to multiply this fraction by sqrt%283%29%2Fsqrt%283%29
which is equivalent to multiplying the fraction by 1 because the denominator of the multiplier
is equal to the numerator.
.
This multiplication is:
.
%281%2Fsqrt%283%29%29%2A%28sqrt%283%29%2Fsqrt%283%29%29=+%281%2Asqrt%283%29%29%2F%28sqrt%283%29%2Asqrt%283%29%29+=+sqrt%283%29%2F%28sqrt%283%29%2Asqrt%283%29%29
.
But in the denominator the multiplication of sqrt%283%29%2Asqrt%283%29 is equal to 3. As a
result the form the answer takes is:
.
sqrt%283%29%2F3
.
And this is the conventional form of the reciprocal of the square root of 3.
.
Hope this helps you to explain the problem to your son.