Question

prove that 3 +√5 is an irrational number​

Answer 1

Answer:

Let us assume that 3+√5 is a rational number.

Let a and b be co-prime numbers having no common factor other than 1, b is not = 0.

a/b=3+√5

a/b-3=√5

a-3b/b=√5

Therefore, we know that √5 is an irrational number

Then a-3b/b should not be equal to √5

So we can say that 3+√5 is an irrational number.

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Answer 2

LHS is not equal to RHS so 3+root 5 is irrational

Hence proved

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