Question

Prove that 2+2 root 3 is irrational.

Answer 1

if it comes in 4 marks question then firstly prove root 3 irrartional then prrof it irrational and if it comes in 2 marks then follow following
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Answer 2

To prove 2+2√3 is irrational no.

If possible let 2+2√3 is a rational no. then it can be in the form of a/b

now,

2+2√3 = a/b

2√3=a/b-2

2√3=(a-2b)/b

√3=(a-2b)/2b br taking 2 on RHS

Here √3 is an irrational no. and (a-2b)/2b is a rational no. because in first we taken a/b as rational no.

∴L.H.S not equal to R.H.S

so our supposition is wrong

Hence, 2+2√3 is an irrational no.