Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 96 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.How many whole numbers lie between 34² and 35²?
2. 2.Which of these is a perfect square? (a) 147 (b) 144 (c) 153
3. 3.What is the smallest whole number by which 150 must be divided to get a perfect square?
4. 4.What is 56²? =
5. 5.What is 34²? =
6. 6.What is √225? =
7. 7.What is √144? =
8. 8.What is √3364? =
9. 9.A square garden has an area of 1024 square m. How long is each side (in m)?
10. 10.What is 49²? =
11. 11.What is √6724? =
12. 12.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 112 must be divided to get a perfect square?
14. 14.How many whole numbers lie between 47² and 48²?
15. 15.Which of these is a perfect square? (a) 293 (b) 307 (c) 289
16. 16.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
17. 17.How many whole numbers lie between 8² and 9²?
18. 18.What is √6400? =
19. 19.How many whole numbers lie between 35² and 36²?
20. 20.Which of these is a perfect square? (a) 1444 (b) 1462 (c) 1519
21. 21.What is the smallest whole number by which 56 must be divided to get a perfect square?
22. 22.What is 87²? =
23. 23.What is √1936? =
24. 24.Which of these is a perfect square? (a) 121 (b) 127 (c) 135
25. 25.A square garden has an area of 289 square m. How long is each side (in m)?
26. 26.What is 17²? =
27. 27.Which of these is a perfect square? (a) 484 (b) 504 (c) 494
28. 28.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
29. 29.How many whole numbers lie between 7² and 8²?
30. 30.What is 72²? =
31. 31.Which of these is a perfect square? (a) 558 (b) 529 (c) 567
32. 32.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
33. 33.What is √1369? =
34. 34.Which of these is a perfect square? (a) 1582 (b) 1521 (c) 1574
35. 35.What is 63²? =
36. 36.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
37. 37.What is the smallest whole number by which 128 must be divided to get a perfect square?
38. 38.How many whole numbers lie between 40² and 41²?
39. 39.A square garden has an area of 36 square m. How long is each side (in m)?
40. 40.What is √9216? =

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