1.

Prove thar 3 + Г5 is irrational​

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Answer:

Let us suppose 3+root 5 is rational.

=>3+root 5 is in the FORM of p/q where p and q are INTEGERS and q is not =0

=>root5=p/q-3

=>root 5=p-3q/q

as p, q and 3 are integers p-3q/3 is a rational number.

=>root 5 is a rational number.

but we know that root 5 is an IRRATIONAL number.

this is an contradiction.

this contradiction has arisen because of our wrong ASSUMPTION that 3+root 5 is a rational number.

hence 3+ root 5 is an irrational number.


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