Question

prove that 2√3+√5 is an irrational number

Answer 1

Yeah it is an irrational no. Becoz the above equation is in root and in which equation root is present are not rational...

Hope it helps

Answer 2

We will prove it by contradiction method ,

If possible let 2√3+√5 a rational number equal to a ,

a=2√3+√5
a^2=(2√3+√5)^2
a^2= (2√3)^2+2(2√3)(√5)+(√5)^2
a^2= 12+4√15+5
a^2=17+4√15
√15=(a^2-17)÷4. (1)

a ia a rational number
a^2 is a rational number
so, (a^2-17)÷4 is also a rational number
so √15 wil also be a rational number (from 1)

But it contradicts the fact that √15 is an irrational number ....

So 2√3+√5 is an irrational number

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