Question

Q. Prove that root2 + 1/root2 is an irrational number...




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Answer 1

Answer:

let √2 + 1/√2 = rational no.

in the form of p/q where ;

q≠0 & the hcf of p and q = 1

Step-by-step explanation:

√2 + 1 = √2p/q

√2 = ( √2p/q ) -1

(√2p/q) - 1 is rational according to our assumptions

but it is equal to √2 = irrational

this is a contradiction to our assumption

therefore √2 = (√2p/q) - 1 = irrational

and so √2 + 1/√2 = irrational

Hence proved

Answer 2

Step-by-step explanation:

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