InterviewSolution
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InterviewSolution
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Which one of the following is correct? The real number `root3(2+sqrt(5))+root3(2-sqrt(5))` is :A. an integerB. a rational number but not an integerC. an irrational numberD. none of the above |
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Answer» Correct Answer - B The given number `root(3)(2+sqrt(5))+root(3)(2-sqrt(5))` can be written as : `=(2+sqrt(5))^(1//3)+(2-sqrt(5))^(1//3)` `2^(1//3)[1+(1)/(2)sqrt(5)]^(1//3)+2^(1//3)[1-(1)/(2)sqrt(5)]^(1//3)` `=2^(1//3)[1+(1)/(6)sqrt(5)+...+1-(1)/(6)sqrt(5)+...]` Thus the given number is a rational number but not an integer. |
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