Question

prove that root 3 + 2 is irrational​

Answer 1

value of root 3 = 1.7320508075..... which is non terminating and non repeating decimal.

and, if we add 2 in root 3 then the value will be 3.7320508075..... which is also non terminating and non repeating decimal.

As we know that the decimal which is non terminating and non repeating is irrational.

Hence, root 3 + 2 is irrational.

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Answer 2

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√3+2
let it be a rational number
then
√3+2=p/q
here p and q are integers and co prime
√3=p/q-2
√3=p-2q/q
as p and q are integers
p-2q/q
will be rational
but √3 is irrational so √3 cannot be equal to p-2q/q
so our assumption is wrong
so √3+2 is irrational




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