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Question
State, whether the following numbers is rational or not:
(√3 − √2)2
Sum
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Solution
(√3 − √2)2
= (√3)2 − 2 (√3)(√2) + (√2)2
= 3 − 2√6 + 2
= 5 − 2√6
5 is rational.
2√6 is irrational (because √6 is irrational).
A rational number minus an irrational number is always irrational.
∴ (√3 − √2)2 irrational number.
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