# Math Help - rationalize expressions

1. ## rationalize expressions

hi i was wondering if any one can help me rationalize these four expressions and if possible show working out so i can understand better, thanks in advance.

1)
8_
√2

2)
16 √9
√12 3√8

3
√2 (1+√2)

4)
1+
√2
1- √2

2. To rationalize is to make the denominator a rational number. Meaning, do not leave a surd or radical number in the denominator.

That's my understanding, so:

8 /sqrt(2)
Multiply both numerator and denominator by sqrt(2),
= [8sqrt(2)] /2

[16sqrt(9)] /[sqrt(12) *3sqrt(8)]

There many ways to do this.
One way is to simplify first all of the radicals.

= [16*3] /[sqrt(4*3) *3sqrt(4*2)]
= 48 /[2sqrt(3) *6sqrt(2)]
= 48 /[12sqrt(3*2)
= 4 /sqrt(6)
Multiply both numerator and denominator by sqrt(6),
= 4sqrt(6) /6

sqrt(2)*[1 +sqrt(2)]
= [sqrt(2) *1 ] +[sqrt(2) *sqrt(2)]