Question

2 +root3 is rational or irrational​

Answer 1

Let us assume that 2+√3 is a rational number which means 2+√3 =r , where "r" is a rational number.

Squaring to both sides , we get

(2+√3)²=r²

2²+2×2×√3+(√3)²=r²

4+4√3+3=r²

7+4√3=r²

4√3=r²-7

√3=r²-7

4

Here, we find that LHS is irrational.But RHS is rational.

This contradicts the fact that 2+√3 is rational.

This means that our assumption was wrong.

Hence, 2+√3 is an irrational number.

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