CBSE Class 10 Answered
Write whether the square of any positive integer can be of the form 3m+2 , where m is a natural number. Justify your answer
Asked by lakshita0708 | 16 Jun, 2019, 09:49: AM
Expert Answer
The numbers are of the form 3q, 3q + 1 and 3q + 2.
(3q)2 = 9q2 = 3(3q2) = 3m, where m is a integer.
(3q + 1)2 = 9q2 + 6q + 1 = 3(3q2 + 2q) + 1 = 3m + 1, where m is a integer.
(3q + 2)2 = 9q2 + 12q + 4, which cannot be expressed in the form 3m + 2.
Therefore, Square of any positive integer cannot be expressed in the form 3m + 2.
Answered by Arun | 16 Jun, 2019, 04:43: PM
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