Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 616 · 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.What is the smallest whole number by which 160 must be divided to get a perfect square?
2. 2.Which of these is a perfect square? (a) 324 (b) 340 (c) 350
3. 3.Which of these is a perfect square? (a) 110 (b) 106 (c) 100
4. 4.A square garden has an area of 1225 square m. How long is each side (in m)?
5. 5.What is √9801? =
6. 6.What is the smallest whole number by which 468 must be divided to get a perfect square?
7. 7.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √8100? =
9. 9.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 324 square m. How long is each side (in m)?
12. 12.What is √1936? =
13. 13.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √6561? =
15. 15.What is √7056? =
16. 16.What is 84²? =
17. 17.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 10² and 11²?
19. 19.Which of these is a perfect square? (a) 408 (b) 400 (c) 403
20. 20.What is 98²? =
21. 21.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 60²? =
23. 23.Which of these is a perfect square? (a) 659 (b) 636 (c) 625
24. 24.What is 79²? =
25. 25.Which of these is a perfect square? (a) 192 (b) 189 (c) 169
26. 26.How many whole numbers lie between 20² and 21²?
27. 27.A square garden has an area of 49 square m. How long is each side (in m)?
28. 28.A square garden has an area of 1600 square m. How long is each side (in m)?
29. 29.What is 55²? =
30. 30.A square garden has an area of 2500 square m. How long is each side (in m)?
31. 31.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
33. 33.What is 49²? =
34. 34.Which of these is a perfect square? (a) 140 (b) 121 (c) 130
35. 35.What is √1024? =
36. 36.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
39. 39.What is √1296? =
40. 40.What is √841? =

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