Question

prove that √2+5 is a irrational number

Answer 1

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Answer 2

To prove √2+5 is a irrational number, proof: let, √2 is rationalon contrary (a and bare co-primes) then √2= a/b , √2b=a *,
equation, now , squaring both sides, we get: 2b^=a^, b^= a^/2 so, since 2 divides a ^ then it will divides a also.,, now since a and b are continue primes, therefore our assumption is wrong hence √2 is a irrational number.
let, √2 +5 is rationalon contrary then√2 +5= a/b where (a and b are continue prime) this implies that √2 =5-a/b and √2= 5b-a/b since √2 is irrational we already proved above this implies that √2 +5 is irrational, hope it helps you