rationalize the denominator?

Question

2/ squared rt[3] +squared rt [2]

Answer 1

if 2 / SQRT(3) + SQRT(2)

then, multiply top and bottom by SQRT(3)

= (2 * SQRT(3)) / SQRT(9) + SQRT(2)
= (2 * SQRT(3)) / 3 + SQRT(2)

if 2 / (SQRT(3) + SQRT(2))

then, multiply top and bottom by (SQRT(3) - SQRT(2))
(opposite operation eliminates middle term)

= 2 * (SQRT(3) - SQRT(2) / (SQRT(9) - SQRT(6) + SQRT(6) - SQRT(4))
= 2 * (SQRT(3) - SQRT(2)) / (3 - 2)
= 2 * (SQRT(3) - SQRT(2))

Jim, http://www.jimpettis.com/wheel/

Answer 2

You need to multiply the numerator and denominator by the conjugate of the denominator. With only one square root, you multiply by the denominator, but with two numbers you will get a middle term. The conjugate is the same as the regular number but with the opposite sign in the middle. So for the sq rt of 3 + the sq rt of 2, the conjugate would be the sq rt of 3 - the sq rt of 2. You still are multiplying the expression by 1, but by multiplying by the conjugate you eliminate the middle term.

Answer 3

Assume that expression is:-
2 / [√3 + √2 ]
= 2 [√3 - √2 ] / [ (√3 + √2 ) (√3 - √2) ]
= 2 (√3 - √2 ) / (3 - 2)
= 2 (√3 - √2 )