Question

Prove that ✓8+5 us irrational number

Answer 1

Let's assume that √8 + 5 is a Rational Number.

Thus, (√8 + 5) € R

Subtract 5 from the above equation,

(√8 +5) - 5 € R - 5

We know that, a rational number subtracted from a rational gives a rational number. Thus, (R-5) is a rational number. That is (R-5)€R

=> (√8+5) -5 €R

=> √8 € R

But, √8 is an irrational number.

Thus, √8 does not belong to R

=> √8 + 5 doesn't belong to R

and, a number which is not rational must be an Irrational Number.

Hence, √8 + 5 is an Irrational number.