Question

Why is the square root of 6 irrational?

Answer 1

becasue it is not well behaved :)

Answer 2

because it never ends and doesnt have a pettern

Answer 3

everytime you try to measure it, it gets fidgety and moves around

Answer 4

thats hilarious amistre64

Answer 5

:)

Answer 6

Let it be rational, and express it as a fraction rt6 = a/b
(a/b)(a/b) = 6
a^2/b^2 = 6
a^2 = 6b^2

Since a is even, there is some integer c that is half of a, or in other words:

2c = a.

(2c)^2 = (2)(3)b^2
2c^2 = 3b^2

Then b is even and a/b is not in its simplest form.

Answer 7

(at least I think so)

Answer 8

whaaat? i did not follow that. luckily, i didnt ask that wuestion

Answer 9

our initial assumption is that a/b is in its simplest form. I showed that both a and b had to be a multiple of 2.

Answer 10

merllet15115: Actually, you did. JethroKuan presented a proof of irrationality which shows 'why' \(\sqrt{2}\) is not rational. :)

Answer 11

Sorry, square root of 6.

Answer 12

ok. i give up. watevs

Answer 13

Where did this question come up? What would you consider a good enough reasoning?

Answer 14

Proof by contradiction should suffice.

Answer 15

i just havent learned, or atleast i dont think i have, any of that stuff

Answer 16

http://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality

Answer 17

And irrational number would by definition mean a number that cannot be presented in the form a/b where a and b are whole numbers. Square root of 6 is irrational since it cannot be written as a fraction. Another feature of irrational numbers is that their decimal forms have an infinite amount of decimals that come up in an unpredictable, non-repeating way. A number with decimal expression 5,67676767676767676767676767676767... is therefore rational since the pair 67 keeps repeating forever. For irrational numbers, it's something complex and non-repeating, for example your \(\sqrt{6}=2.4494897427831780981972840747058913919659474806566701284326...\)