State whether following numbers are rational or irrational.(i) (ii)

(i)

We have,

We know √144 = 12 and √100 = 10

So,

= 1.2

Every terminating decimal is a rational number, so 1.2 is a rational number.

(ii)

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.

Since, the product of a rational and an irrational is an irrational number.

Therefore, is an irrational.

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