Question

Prove 8+ root 11 is irrational

Answer 1

Answer:

it can be solved indirect method of proof.

Answer 2

Answer:

let √5 + √11 be in the form of a/b where a and b are co prime nos and integers

√5 +√11=a/b

√5=a/b-√11

we know that √5 is irrational (as explained below)

therefore √5+√11 is also irrational

hence proved.

Let us assume that √5 is a rational number.

we know that the rational numbers are in the form of p/q form where p,q are integers.

so, √5 = p/q

    p = √5q

we know that 'p' is a rational number. so √5 q must be rational since it equals to p

but it does'nt occurs with √5 since its not an integer

therefore, p =/= √5q

this contradicts the fact that √5 is an irrational number

hence our assumption is wrong and √5 is an irrational number.

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