Question

show that √11 is not a rational number​

Answer 1

Answer:

Step-by-step explanation:

Let √11 be rational

∴ √11 = p/q where p and q are co prime and q≠ 0

Square both the sides, 11 = p²/q²

⇒ 11 q² = p²

Hence p is divisible by 11

Let p = 11 r

Square both sides:-

p² = 121 r²

11 q² = 121 r²

q² = 11 r²

∴ q is divisible by 11

⇒ both p and q are divisible by 11

But this contradicts that p and q are co prime. Hence our assumption is wrong.

∴ √11 is irrational

Answer 2

√11= 3.31662479

it cannot be rational number because the numbers which are written in p/q for and they are integers and q @not 0.

3.31662479/3.