Question

prove that root 5 + root 2 is irrational​

Answer 1

Answer:

because this is not in the form of a/b

Answer 2

Answer:

let root 5 + root 2 be rational number.

A rational number is in p/q form.

root 5 + root 2 = p/q

squaring on both sides

(root 5 + root 2)^2 = (p/q)^2

(root 5)^2 + (root 2)^2 + 2 (root 5) ( root 2) = p^2/q^2

5+2+2 (root10) = p^2/q^2

7 + 2 (root 10) = p^2/q^2

2 (root 10) =p^2/q^2 - 7

root 10 = ( p^2 - 7q^2)/2q

p and q are integers (p^2-7q^2)/2q is a rational number.

then root 10 is also a rational number

but root 10 is a irrational number

our supposition is false

root 5 + root 2 is a irrational number

hence proved

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