Prove that √2 + √5 is irrational .
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let us assume √2+√5 is a rational number
we can find a,b are Co primed
√2+√5=a/b
squaring on both sides
(√2+√5)^= (a/b)^
2+5+2(√2)(√5)= a^/b^
7+2√10=a^/b^
2√10= a^/b^ -7
2√10 = a^-7b^/b^
√10=a^-7b^/2b°
if a,b are integer than RHS rational if RHS is rational than LHS √10 is rational
But this is a fact that √10 is irrational
√10 is irrational
√2+√5 is irrational.
hope this help you