Aasoka Mathematics Practise 3.1 Solutions | Squares and Square roots Class 8

Chapter 3 Squares and Square Roots
Practise: 3.1
Class 8
Book Name: Mathematics ( AASOKA Edition)
Question Solved:
1. The following numbers are not perfect squares. Give reasons for each.
(i)3542
(ii) 900000
(iii) -289
(iv) 64000
(v) 31057
2. Without finding the squares, find the units digit in the squares of the following numbers.
(i) 352
(ii) 9377
(iii) 285
(iv) 4626
(v) 999
3. Without actual calculations, find the following sums.
(i) 1+3+5+7+9 + 11
(ii) 1+3+5 +7+9+11 + 13 + 15 + 17 + 19+21
(iii) 11+13 + 15 + 17 +19 +21 +23 +25 +27 +29
(iv) 13 +15 +17+ 19 +21 +23
4. Categorise the following numbers according to whether their squares are even or odd.
(i) 761
(ii) 1007
(iii) 4444
(iv) 4368
(v) 2893
5. Express the following square numbers as the sum of two consecutive natural numbers.
(i) 441
(ii) 289
(iii) 4225
(iv) 24011
(v) 4489
6. Using dots, draw a square of side 7 dots, and hence write 7² as sum of wo triangular numbers.
7. Find how many non- square natural numbers lie between the following pairs:
(i) 7² and 8²
(ii) 10² and 11²
(iii) 14² and 15²
(iii) 21² and 22²
8. Can square of 391 be 9891? Justify your answer.
9. A number can be written in the form 3m +2, for some natural number m. Can this number be a perfect
square?
10. Anumber can be written in the form 4m +3, for some natural number m. Can this number be a perfect
square?
11. Without finding the squares, evaluate each of the following
(i) 49² - 1 (ii) 61² - 1 (iii) 199² - 1
12. Without finding the squares, evaluate each of the following
(i) 16²- 15² (ii) 221² - 220² (iii) 59² - 58²
13. Observe each of the patterns given below and fill in the missing numbers/digits.
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