show that root 5 is irrational
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We will prove whether √5 is irrational by contradiction method.
Let √5 be rational
It can be expressed as √5 = a/b ( where a, b are integers and co-primes.
√5 = a/b
5= a²/b²
5b² = a²
5 divides a²
By the Fundamental theorem of Arithmetic
so, 5 divides a .
a = 5k (for some integer)
a² = 25k²
5b² = 25k²
b² = 5k²
5 divides b²
5 divides b.
Now 5 divides both a & b this contradicts the fact that they are co primes.
this happened due to faulty assumption that √5 is rational. Hence, √5 is irrational.
Let √5 be rational
It can be expressed as √5 = a/b ( where a, b are integers and co-primes.
√5 = a/b
5= a²/b²
5b² = a²
5 divides a²
By the Fundamental theorem of Arithmetic
so, 5 divides a .
a = 5k (for some integer)
a² = 25k²
5b² = 25k²
b² = 5k²
5 divides b²
5 divides b.
Now 5 divides both a & b this contradicts the fact that they are co primes.
this happened due to faulty assumption that √5 is rational. Hence, √5 is irrational.
rosy43:
im so sorry that i had to disturb u
u could pls send it in paper with proper steps because tom i have ut on this
sorry dear! I hope you can read the answer ,it's not too hard to understand
ok by reading it now go to know
thanks
ven if u could do root 7 also plsss
even*
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