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.
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.
Any natural number ending in 0, 1, 4, 5, 6 or 9 can be or cannot be a square-number. Five such numbers are:
56790, 3671, 2454, 76555, 69209
Property 2. If a number has 1 or 9 in the unit’s place, then its square ends in 1.
For example:
(1)2 = 1, (9)2 = 81, (11)2 = 121, (19)2 = 361, (21)2 = 441.
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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