Rationalizing Radicals

Ok, now for the exciting topic of rationalizing radicals.

Example #1
__3__
√2+1

STEP ONE

Multiply both the numerator and the denominator by the conjugate. This is the same as the denominator, just with the second term's sign reversed. If there is only one sign in the denominator, don't change the sign.

__3__ (√2-1)
√2+1 (√2-1)

=

3√2-3
_____
2-1

STEP TWO

Solve the rest of the problem. REMEMBER TO REDUCE (if possible)!

3√2-3
_____
2-1

3√2-3
_____
1

= 3√2-3

Do the same for the rest.

Example #2

(√5 + √2)(√5-√2)

multiply the terms together

√2x - √10 +3√2-3
√2x- √10 + √10 - √4
5-2=3

Example #3

_7_ (√3-1) <-----conjugates
√3+1(√3-1) <-----

7√3 - 7
_____
3 - 1

= 7√3-7
______

2

Example #4

__2__ (√5 + 2)
√5 - √2 (√5+2)

2√5 + 2√2
_______
√25 + √10 √10 - √4

2√5+2√2
_______
5-2

2√5 + 2√2
________

3

Example #5

__15__ (√14+5)
√14 - 5 (√14+5)

15√14 + 75
__________
√196 + 5√14 - 5√14 - 25

15 √14 +75
_________
14 - 25

15√14 + 75
_______
-11

Example #6

4√15 (3√15 - 8)
______
3√15 + 8 (3√15-8)

12√225 - 32 √15
____________
9√225 - - 24√15 +24 √15 - 64

180 - 32√15
________
135 - 64

180 - 32√15
________
71

The next blogger is
Ana