Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 714 · 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 17²? =
2. 2.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
3. 3.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the smallest whole number by which 1134 must be multiplied to get a perfect square?
5. 5.Which of these is a perfect square? (a) 339 (b) 324 (c) 330
6. 6.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 961 square m. How long is each side (in m)?
8. 8.What is √400? =
9. 9.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
10. 10.A square garden has an area of 36 square m. How long is each side (in m)?
11. 11.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
13. 13.What is √625? =
14. 14.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
15. 15.What is √784? =
16. 16.What is 12²? =
17. 17.Which of these is a perfect square? (a) 132 (b) 130 (c) 121
18. 18.What is 54²? =
19. 19.Which of these is a perfect square? (a) 171 (b) 175 (c) 169
20. 20.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
21. 21.A square garden has an area of 169 square m. How long is each side (in m)?
22. 22.How many whole numbers lie between 29² and 30²?
23. 23.What is 51²? =
24. 24.How many whole numbers lie between 31² and 32²?
25. 25.A square garden has an area of 784 square m. How long is each side (in m)?
26. 26.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 720 (b) 727 (c) 676
29. 29.A square garden has an area of 400 square m. How long is each side (in m)?
30. 30.What is 98²? =
31. 31.What is the smallest whole number by which 350 must be divided to get a perfect square?
32. 32.How many whole numbers lie between 44² and 45²?
33. 33.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
34. 34.What is 45²? =
35. 35.What is the smallest whole number by which 640 must be divided to get a perfect square?
36. 36.What is 65²? =
37. 37.How many whole numbers lie between 16² and 17²?
38. 38.Which of these is a perfect square? (a) 734 (b) 729 (c) 735
39. 39.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
40. 40.What is the smallest whole number by which 325 must be multiplied to get a perfect square?

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