# Proof that 2√3+√5 is an irrational number also check whether (2√3+√5) (2√3-√5) is rational or irrational number

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Let us assume 2√3+√5 as rational.

we can get integers a&b in the form a/b.

2√3+√5=a/b

squaring obs

(2√3+√5)sq= (a/b)sq

(2√3)sq +(√5)sq+2(2√3×√5)= (a)sq/(b)sq

20+5+4+2√15=(a)sq/(b)sq 2√15=(a)sq/(b)sq - 29

since a&b are integers 2√15 is rational

but this contradicts that 2√3+√5 is irrational.

this contradiction has arisen due to the incorrect assumption that 2√3+√5 is rational .

hence it is irrational.

we can get integers a&b in the form a/b.

2√3+√5=a/b

squaring obs

(2√3+√5)sq= (a/b)sq

(2√3)sq +(√5)sq+2(2√3×√5)= (a)sq/(b)sq

20+5+4+2√15=(a)sq/(b)sq 2√15=(a)sq/(b)sq - 29

since a&b are integers 2√15 is rational

but this contradicts that 2√3+√5 is irrational.

this contradiction has arisen due to the incorrect assumption that 2√3+√5 is rational .

hence it is irrational.