0 like 0 dislike
0 like 0 dislike
How do you rationalize this? (move irrationals out of the denominator)
by

5 Answers

0 like 0 dislike
0 like 0 dislike
Just do it in two steps

1 + root2 + root3 = (1 + root2) + root3
0 like 0 dislike
0 like 0 dislike
Can’t figure out what to multiply the top and bottom by to get the irrationals out of the bottom :/
0 like 0 dislike
0 like 0 dislike
(1+sqrt(2)+sqrt(3))(1-sqrt(2)-sqrt(3))=-4-2sqrt(6)

so you'd have to multiply again, this time by -4+2sqrt(6)

in general the "conjugate" of a+bX+cY+.... will always be a-bX-cY-.... (similar to how complex numbers work)

where a,b,c,... are from the base field and X,Y,... are the algebraic numbers you extend the field by.
0 like 0 dislike
0 like 0 dislike
1/(1+sqrt2+sqrt3))×

(1+sqrt2-sqrt3)/(1+sqrt2-sqrt3)=

(1+sqrt2-sqrt3)/(1+2sqrt2+2-3)=

(1+sqrt2-sqrt3)/(2sqrt2)

Multiply by sqrt2/sqrt2:

**(sqrt2+2-sqrt6)/4**
0 like 0 dislike
0 like 0 dislike
OP, if you get the decimal approximation of the original expression on your calculator, you can do the same for your answer and compare them.

Related questions

0 like 0 dislike
0 like 0 dislike
4 answers
TommyBanks8 asked Jun 21
Recently i started Problems in Mathematical Analysis 1: Real Numbers, Sequences and Series by Kaczor Nowak. Its problems are very tough. So i need some books which have a...
TommyBanks8 asked Jun 21
0 like 0 dislike
0 like 0 dislike
4 answers
Tamilmirror asked Jun 21
I want to do this rhubarb wine recipe but I have 5.649 kg of rhubarb instead of 1.25kg in the recipe; can anyone tell me how much sugar I need to add to my amount and wha...
Tamilmirror asked Jun 21
0 like 0 dislike
0 like 0 dislike
2 answers
Figure1 asked Jun 21
What does Euler characteristic tell us about topological spaces? For example, what do we find out from the fact that the Euler characteristic of a sphere is 2 and of a to...
Figure1 asked Jun 21
by Figure1
0 like 0 dislike
0 like 0 dislike
6 answers
repreve asked Jun 21
How do you calculate the intersections of two parabolas that are not parallel in their axis? For example the ones you can see on the picture below. Blue parabola is y = (...
repreve asked Jun 21
by repreve
0 like 0 dislike
0 like 0 dislike
0 answers
BirhanV asked Jun 21
Say I have a 40 card deck. I have two different cards, and three copies of each card. It’s well shuffled together. What is the probability, and how do you calculate it,...
BirhanV asked Jun 21
by BirhanV

24.8k questions

103k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!