prove that 11underroot is irrational
Answers
Root 11 can be proved as irrational as because it's value is non-terminating and non-repeating so we can say... ✌✌
✔️✔️ ANSWER ✔️✔️
✔️✔️prove that 11underroot is irrational✔️✔️
✔️Let us assume that √11 is rational
✔️Therefore,it can be expressed in the form p/q where q ≠0 and (p,q)=1 and p and q are integers
✔️p/q=√11
Therefore,
✔️p^2/q^2=11. …(squaring both sides)
✔️p^2=11(q^2)
✔️Now, 11(q^2)= a perfect square
1
✔️11 is not a factor of q
Therefore,
p^2=11(q^2) … (q,11)=1
p=q√11. … (taking square root on both sides)
But,p is an integer
Therefore, contradiction.
2
✔️11 is a factor of q.
Let's say q=11k where k is any non-zero integer
Therefore,
q^2 = (11k)^2
q^2=11 ^2 *k^2
q^2*11 =11^3 *k^2
Therefore p =√(11^3 *k^2)=11k*√11
It is irrational.
✔️But p is integer
Therefore, contradiction in both cases
✔️Therefore, √11 is irrational
✔️ proved
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