Q. 83.7( 65 Votes )
State whether following numbers are rational or irrational.
We know √144 = 12 and √100 = 10
Every terminating decimal is a rational number, so 1.2 is a rational number.
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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