Examine, whether (2 + √2)2 is rational or irrational.

1.	Examine, whether (2 + √2)2 is rational or irrational.
Answer» (2 + √2)² = 2² + (√2)² + 2 x 2 x √2 [using identity, (a+b)² = a² + b² + 2ab] = 4 + 2 + 4√2 = 6 + 4√2 Here, 6 is a rational number but 4√2 is an irrational number. Since, the sum of a rational and an irrational number is an irrational number, therefore, (2+ √2)² is an irrational number.

Answer»

(2 + √2)²

= 2² + (√2)² + 2 x 2 x √2 [using identity, (a+b)² = a² + b² + 2ab]

= 4 + 2 + 4√2

= 6 + 4√2

Here, 6 is a rational number but 4√2 is an irrational number. Since, the sum of a rational and an irrational number is an irrational number, therefore, (2+ √2)² is an irrational number.

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Examine, whether (2 + √2)2 is rational or irrational.

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