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Write any three irrational number between -3 and 1/3 |
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Answer» At first , let's introduce 4 rational numbers between 1/3 & 3/4 . 1/3 = 4/12 3/4 = 9/12 Therefore , 4 such rational numbers are : 5/12 , 6/12 , 7/12 , 8/12 Now , between any two integers a & b , there exists √(ab) , their geometric mean . Therefore , an irrational number between 4/12 & 5/12 = √20/12 = 2√5/12 = √5/6 . Similarly , another irrational number between 5/12 & 6/12 = √30/12 Proceeding thus , we get other THREE irrational numbers in SUCCESSIVE INTERVALS : √42/12 , √56/12 (=√14/6) , √72/12 (=1/√2) Therefore , we have , 1/3 < √5/6 < √30/12 < √42/12 < √14/6 < 1/√2 < 3/4 . There are HOWEVER , other ways of doing this sum |
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