Identify which of the following is not a rational number: - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
${(\sqrt{2})}^{2}$
B
$\sqrt{2} + 3$
C
$\sqrt{2} - 3$
D
${(\sqrt{2})}^{4}$

Solution:

A rational number is a number in the form of p/q where p and q are integers and q is not equal to 0

${(\sqrt{2})}^{2} i s e q u a l t o 2 w h i c h c a n b e r e p r e s e n t e d b y 2 / 1 . A l s o, {(\sqrt{y})}^{x} w h e r e y i s i n t e g e r a n d x i s e v e n n u m b e r, i t w i l l b e r a t i o n a l n u m b e r . I f x i s o d d, i t w i l l b e i r r a t i o n a l n u m b e r . \sqrt{2} i s a n i r r a t i o n a l n u m b e r a n d i f a n i r r a t i o n a l n u m b e r i s a d d e d t o a n y n u m b e r, t h e n u m b e r w i l l b e i r r a t i o n a l n u m b e r .$