Radical Expressions homework help?

Question

1
_______
3 - 2^(1/2)

Rationalize the denominator (sorry i dont know how to type square roots on the computer)...

The book's answer is :

1+2^(1/2).
________
7
I dont understand how they got 7 for the denominator. I understand how the numerator came about. I got -6 for the denominator.... please help..

i mean i got 1 for the denominator

Answer 1

1 / (3 - √2)
(3 + √2) / ((3 - √2)(3 + √2)
(3 + √2) / (9 - 2)
(1/7) (3 + √2)

Answer 2

You rationalize the denominator by multiplying by its conjugate -- the expression with the other sign between the terms. (This will generate the difference of two squares, and make the radicals all drop out).
So you multiply both top and bottom by (3 + √2)
{(1)(3 + √2)} / {(3 - √2)(3 + √2)}
= (3 + √2) / (9 + 3√2 -3√2 - 2)
= (3 + √2) / (9 - 2) -- (since the radicals in the middle cancel, and (-√2)(√2) = -2 -- the beauty of the diffence of two squares)
So the correct answer is (3 + √2) / 7
or in the fractional exponent form you used : {3 + 2^(1/2)} / 7
Try using Alt 251 to get the radical sign√. This works on many (but not all) computers.

Answer 3

1/(3-√2) to rationalize multiply by (3+√2)/(3+√2)

(3 + √2)/(9 - 2)
(3 + √2)/7