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Short Answer1. Prove that√3 +√7 is an irrational number |
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Answer» ONG>ANSWER: We have to prove that 3+ 7
is IRRATIONAL. Let us assume the opposite, that 3+ 7
is rational. Hence 3+ 7
can be WRITTEN in the form b a
where a and b are co-prime and b =0 Hence 3+ 7
= b a
⇒ 7
= b a
−3 ⇒ 7
= b a−3b
where 7
is irrational and b a−3b
is rational. Since,rational = irrational. This is a contradiction. ∴ Our assumption is incorrect. Hence 3+ 7
is irrational. Hence proved. |
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