Question

Root 25 + root 5 is a rational no ? justify u r answer

Answer 1

Hey mate,

Let us assume to the contrary that √25+√5 is rational. so we can find coprimes a and b such that √25+√5=a/b,where b≠0

√25+√5=a/b

as√25=5,

5+√5=a/b

√5=a-5b/b

since a,b and 5 are integers,a-5b/b is rational. and thus,√5 is also rational. but this contradicts the fact that √5 is irrational. this contradiction has arisen because of our incorrect assumption that √25+√5 is rational. so,√25+√5 is irrational.

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Answer 2

Root 25= 5

=> 5 +root 5 is a irrational no.