Question

Why is 3 plus root 13 an irrational number

Answer 1

Let us assume to, the contrary, that 3+√13 is rational . That is we can find integers photo and q(q not equal to 0) such that

3+√13 =p/q

√13 = p/q-3

1. Since, p and q are integers we get p - 3q/q is rational ,and so √13 is Rational.

But this contradicts the fact that√13 is rational.

So,we conclude that 3+√13 irrational no.

Or another than 1

√13 = p/q-3

As we know that √ 13 is an irrational no. And since an irrational no can't be equal to rational no. Therefore3+ √13 is an irrational no.