prove that √11 is irrational
Answers
gLet as assume that √11 is a rational number. A rational number can be written in the form of p/q where q ≠ 0 and p , q are non negative number. Hence Our assumption is Wrong √11 is an irrational number . Irrational numbers are which numbers that can't be expressed as p/q form that are irrational numbers.
Answer:
1. Assume √11 is rational
2. Express √11 = p/q ( p,q are integers and co-prime)
3. Squaring both sides => 11 = p^2/q^2
=> 11 * q^2 = p^2. -----(ie, p^2 is a multiple of 11).
4. p can be expressed as 11*m (m is an integer).
5. Substitute p = 11m in step 3
11 q^2 = 11 ^2 . m^2
q^2 = 11* m^2 => q is a multple of 11
6. we conclude that p and q has a common factor 11 ( from step 3, 5)
7. This contradicts our statement p,q are co-prime and hence √11 is irrational.