Examine, whether the following numbers are rational or irrational:
(i) (√2 + 2)2
(ii) (2-√2)x(2 +√2)
(iii) (√2 +√3)2
(iv)
(i) (√2 + 2)2 = (√2)2 + 2√2x2 + (2)2 = 2 + 4√2 + 4 = 6 + 4√2 .
... It is an irrational number.
(ii) (2- √2)x(2 + √2) = (2)2 - (√2)2 = 4 - 2 = 2 .
... It is a rational number.
(iii) (√2 + √3)2 = (√2)2 + 2√2x√3 + (√3)2 = 2 + 2√6 + 3 = 5 + 2√6
... It is an irrational number.
(iv)
= 
= √2
... It is an irrational number. ... It is an irrational number.
(ii) (2- √2)x(2 + √2) = (2)2 - (√2)2 = 4 - 2 = 2 .
... It is a rational number.
(iii) (√2 + √3)2 = (√2)2 + 2√2x√3 + (√3)2 = 2 + 2√6 + 3 = 5 + 2√6
... It is an irrational number.
(iv)
= = √2AI is thinking…
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is not a rational number and 
is not a rational number. 