Short Answer Type
Long Answer Type1. Can we say whether the following numbers are perfect squares? How do we know?
(i) 1057 (ii) 23453 (iii) 7928
(iv) 222222 (v) 1069 (vi) 2061
Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.
(i) 1057
∵ The ending digit is 7 (which is not one of 0, 1, 4, 5, 6 or 9)
∴ 1057 cannot be a square number.
(ii) 23453
∵ The ending digit is 3 (which is not one of 0, 1, 4, 5, 6 and 9)
∴ 23453 cannot be a square number.
(iii) 7928
∵ The ending digit is 8 (which is not one of 0, 1, 4, 5, 6 and 9)
∴ 7928 cannot be a square number.
(iv) 222222
∵ The ending digit is 2 (which is not one of 0, 1, 4, 5, 6 or 9)
∴ 222222 cannot be a square number,
(v) 1069
∵ The ending digit is 9.
∴ It may or may not be a sqaure number.
Also, 30 x 30 = 900
31 x 31 = 691
32 x 32 = 1024
33 x 33 = 1089
i.e. No natural number between 1024 and 1089 is a square number.
∴ 1069 cannot be a square number.
(vi) 2061
∵ The ending digit is 1
∴ It may or may not be a square number.
∵ 45 × 45 = 2025
and 46 × 46 = 2116
i.e. No natural number between 2025 and 2116 is a square number.
∴ 2061 is not a square number.
We can write many numbers which do not end with 0, 1, 4, 5, 6 or 9. (i.e. which are not square number). Five such numbers can be:
1234, 4312, 5678, 87543, 1002007.
Short Answer TypeWrite five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.
Which of the following numbers would have digit 6 at unit place.
(i) 192 (ii) 242 (iii) 262
(iv) 362 (v) 342
What will be the “one’s digit” in the square of the following numbers?
(i) 1234 (ii) 26387 (iii) 52698
(iv) 99880 (v) 21222 (vi) 9106
The square of which of the following numbers would be an odd number/an even number?
Why?
(i) 727 (ii) 158 (iii) 269 (iv) 1980
What will be the number of zeros in the square of the following numbers?
(i) 60 (ii) 400
How many non-square numbers lie between the following pairs of numbers:
(i) 1002 and 1012 (ii) 902 and 912
(iii) 10002 and 10012
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