SOLUTION: 2/sqrt[3] + sqrt[2] Can you help me rationalize the denominator? I really apprecuate your help. It would help so much if you could show me how you do this.

Algebra ->  Rational-functions -> SOLUTION: 2/sqrt[3] + sqrt[2] Can you help me rationalize the denominator? I really apprecuate your help. It would help so much if you could show me how you do this.      Log On


   

Question 86383This question is from textbook Intermediate Algebra
: 2/sqrt[3] + sqrt[2]
Can you help me rationalize the denominator? I really apprecuate your help. It would help so much if you could show me how you do this. This question is from textbook Intermediate Algebra

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2/sqrt[3] + sqrt[2]
---------
Multiply numerator and denominator by (sqrt3 - sqrt2) to get:
[2(sqrt3 - sqrt2)]/[3-2]
=2(sqrt3 - sqrt2)
=======================
Why does this work?
Because (sqrt3+sqrt2)(sqrt3-sqrt2) = 3+sqrt6-sqrt6-2 = 3-2=1
===============
Cheers,
Stan H.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28sqrt%283%29+%2B+sqrt%282%29%29
Can you help me rationalize the denominator? I really apprecuate your help. It
would help so much if you could show me how you do this.

Form the conjugate surd of the denominator:
1. Copy the first term
2. Copy the second term with the sign changed.

The conjugate surd of the denominator sqrt%283%29%2Bsqrt%282%29 is
sqrt%283%29+-+sqrt%282%29.  Write it over itself to form a 
fraction equal to 1:

%28sqrt%283%29+-+sqrt%282%29%29%2F%28sqrt%283%29+-+sqrt%282%29%29

Multiply the original eqpression by that fraction.  It doesn't
change the value because the fraction equals 1.

    
2%2F%28sqrt%283%29+%2B+sqrt%282%29%29×%28sqrt%283%29+-+sqrt%282%29%29%2F%28sqrt%283%29+-+sqrt%282%29%29



FOIL out the denominator:

+2+%28sqrt%283%29+-+sqrt%282%29+%29%2F%283+%2B+sqrt%286%29-sqrt%286%29-2%29++

Cancel the terms in sqrt%286%29 in the bottom

+2+%28sqrt%283%29+-+sqrt%282%29+%29%2F%283-2%29++

+2+%28sqrt%283%29+-+sqrt%282%29+%29%2F1++

+2+%28sqrt%283%29+-+sqrt%282%29+%29++

You can multiply that out if you like and get

2sqrt%283%29+-+2sqrt%282%29

Edwin