Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 168 · 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 960 must be multiplied to get a perfect square?
2. 2.What is √400? =
3. 3.A square garden has an area of 676 square m. How long is each side (in m)?
4. 4.What is 85²? =
5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
6. 6.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
7. 7.What is the smallest whole number by which 18 must be divided to get a perfect square?
8. 8.Which of these is a perfect square? (a) 110 (b) 108 (c) 100
9. 9.Which of these is a perfect square? (a) 1296 (b) 1308 (c) 1351
10. 10.What is √1225? =
11. 11.What is 81²? =
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
14. 14.Which of these is a perfect square? (a) 1631 (b) 1623 (c) 1600
15. 15.Which of these is a perfect square? (a) 784 (b) 787 (c) 793
16. 16.What is 48²? =
17. 17.What is the smallest whole number by which 52 must be divided to get a perfect square?
18. 18.A square garden has an area of 1764 square m. How long is each side (in m)?
19. 19.What is 51²? =
20. 20.Which of these is a perfect square? (a) 225 (b) 252 (c) 226
21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
22. 22.A square garden has an area of 484 square m. How long is each side (in m)?
23. 23.What is 62²? =
24. 24.What is 91²? =
25. 25.What is √7056? =
26. 26.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
27. 27.A square garden has an area of 625 square m. How long is each side (in m)?
28. 28.What is √289? =
29. 29.What is √1681? =
30. 30.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √484? =
32. 32.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
33. 33.A square garden has an area of 225 square m. How long is each side (in m)?
34. 34.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
35. 35.Which of these is a perfect square? (a) 1426 (b) 1369 (c) 1394
36. 36.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
37. 37.What is the smallest whole number by which 468 must be divided to get a perfect square?
38. 38.What is √9025? =
39. 39.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
40. 40.What is the smallest whole number by which 27 must be divided to get a perfect square?

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