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07 Feb 2022, 00:11
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Just saw a question in DS, and thought some information might help in similar questions.
In DS, you may get some question related to PERFECT square. Remember, in such questions, you may not be able to answer in affirmative, but certain things can give a NO for sure.
Few of such things that come to my mind immediately are:-
1) If a number ends in, that is the units digit is, 2, 3, 7 or 8, the number will not be a perfect square. For example - abc02 or abcd67
2) If the unit's digit is 0 but the tens digit is not 0, the number will be a multiple of 10 but not of 100. For example - abc20 or abcd50
3) If the unit's digit is 5 but the tens digit is not 2, the number will be a multiple of 5 but not of 25. For example - abc15 or abcd65
4) If the sum of digits is multiple of 3 but not of 9, the answer will again be NO. For example - 120102 or 2000004
5) If the number is even, but the last two digits are not multiple of 4, it will not be a perfect square. For example - abc02 or abcd34
6) If total number of factors is even, the answer is NO.
In DS, you may get some question related to PERFECT square. Remember, in such questions, you may not be able to answer in affirmative, but certain things can give a NO for sure.
Few of such things that come to my mind immediately are:-
1) If a number ends in, that is the units digit is, 2, 3, 7 or 8, the number will not be a perfect square. For example - abc02 or abcd67
2) If the unit's digit is 0 but the tens digit is not 0, the number will be a multiple of 10 but not of 100. For example - abc20 or abcd50
3) If the unit's digit is 5 but the tens digit is not 2, the number will be a multiple of 5 but not of 25. For example - abc15 or abcd65
4) If the sum of digits is multiple of 3 but not of 9, the answer will again be NO. For example - 120102 or 2000004
5) If the number is even, but the last two digits are not multiple of 4, it will not be a perfect square. For example - abc02 or abcd34
6) If total number of factors is even, the answer is NO.
07 Feb 2022, 01:12
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Thanks chetan2u for the above points . This is very helpful!
Wanted to check if we can summarize point 2 to 5 as -
If a perfect square '\(n^2\)' is divisible by a prime 'p', it will also be divisible by \(p^2\).
Wanted to check if we can summarize point 2 to 5 as -
If a perfect square '\(n^2\)' is divisible by a prime 'p', it will also be divisible by \(p^2\).
07 Feb 2022, 06:54
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AbhiroopGhosh
Thanks chetan2u for the above points . This is very helpful!
Wanted to check if we can summarize point 2 to 5 as -
If a perfect square '\(n^2\)' is divisible by a prime 'p', it will also be divisible by \(p^2\).
Wanted to check if we can summarize point 2 to 5 as -
If a perfect square '\(n^2\)' is divisible by a prime 'p', it will also be divisible by \(p^2\).
Yes, that would be true
However, equally important is that to know what numbers can be perfect square and what not. The points above are basically talking of number properties.
