Examine, whether the following numbers are rational or irrational:

(i) (ii) 5-√2

(i)

We have,

= 2 + 2√6 + 3

= 5 + 2

The sum of a rational number and an irrational number is irrational number. Therefore, it is an irrational number.

(ii) 5-√2

Now √2,

Consider,

Where p and q are the integers having no common factor and q≠0.

So p² is an even integer.

⇒ p is an even integer.

Let p = 2m

So p² = 4m²

⇒ 2q² = 4m²

⇒ q² = 2m²

q² is an even integer.

So, q is an even integer.

Since both p and q have common factor 2 and are even. This contradicts the assumption that p and q have no common factor.

Hence √2 is irrational number.

The difference of a rational number and an irrational number is an irrational number.

Therefore, 5 - is an irrational number.