Question

Prove that√11 is given as an irrational number

Answer 1

Step-by-step explanation:

Let us assume that √11 is rational.

so it must be in the form a/b.

√11=a/b

√11b=a

squaring both sides, we get

11b^2= a^2 ----------------- eq. 1

therefore, 11 is the factor of a.

Now,

for any integer c,

let, 11c=a

squaring both sides we get,

121 c^2= a^2 --------------eq. 2

From eq. 1 and 2 we get,

121 c^2= 11b^2

11c^2=b^2

so 11 is the factor of b.

so a and b are factors of each other.

But if they would be rational, they should not be the factor.

so, √11 is irrational.

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