Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 166 · 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 sum of the first 26 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 100 square m. How long is each side (in m)?
3. 3.What is 67²? =
4. 4.What is 62²? =
5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
6. 6.Which of these is a perfect square? (a) 1325 (b) 1296 (c) 1367
7. 7.Which of these is a perfect square? (a) 222 (b) 217 (c) 196
8. 8.What is √5184? =
9. 9.What is 34²? =
10. 10.A square garden has an area of 225 square m. How long is each side (in m)?
11. 11.Which of these is a perfect square? (a) 121 (b) 132 (c) 141
12. 12.Which of these is a perfect square? (a) 108 (b) 100 (c) 107
13. 13.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √6724? =
15. 15.What is the smallest whole number by which 108 must be divided to get a perfect square?
16. 16.What is 88²? =
17. 17.A square garden has an area of 1156 square m. How long is each side (in m)?
18. 18.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the smallest whole number by which 180 must be divided to get a perfect square?
20. 20.A square garden has an area of 1089 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
22. 22.What is 47²? =
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 237 (b) 225 (c) 245
25. 25.What is √1225? =
26. 26.What is 19²? =
27. 27.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
28. 28.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
29. 29.What is 61²? =
30. 30.What is the smallest whole number by which 44 must be divided to get a perfect square?
31. 31.Which of these is a perfect square? (a) 315 (b) 289 (c) 301
32. 32.Which of these is a perfect square? (a) 676 (b) 712 (c) 678
33. 33.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
34. 34.What is √5625? =
35. 35.What is 70²? =
36. 36.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 84²? =
38. 38.A square garden has an area of 784 square m. How long is each side (in m)?
39. 39.What is 31²? =
40. 40.A square garden has an area of 676 square m. How long is each side (in m)?

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