- #1
PcumP_Ravenclaw said:Dear All,
Please help me understand how ## \sqrt{2} ## divide by 0 is rational as stated in the excerpt from alan F beardon's book?
PcumP_Ravenclaw said:Hey PeroK, I think this is what you mean??
##
a^2 - 2b^2 = 0
##
can be written as
##
(a + \sqrt{2}b)(a - \sqrt{2}b) = 0
##
here note that a and b are rational numbers ## {a + b√2 : a, b ∈ Q}, ##
so either ## (a + \sqrt{2}b)## or ## (a - \sqrt{2}b) ## must equal 0.
lets say ## (a - \sqrt{2}b) = 0 ## then ## \sqrt{2} = a/b ## which is a contradiction so ## (a - \sqrt{2}b) = 0 ## cannot happen.
The square root of 2 divided by 0 is undefined.
This is because division by 0 is undefined in mathematics. It is considered to be a mathematical error and does not produce a meaningful result.
No, it cannot be rational because rational numbers are defined as numbers that can be expressed as a ratio of two integers, and dividing by 0 does not produce a rational number.
No, there is no solution for this expression as division by 0 is undefined and does not have a meaningful answer.
Dividing by 0 is often associated with infinity because as the divisor (in this case, 0) gets closer and closer to 0, the resulting quotient gets larger and larger, approaching infinity. However, this does not mean that dividing by 0 is equal to infinity, as it is still undefined.