Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 201 · 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.A square garden has an area of 900 square m. How long is each side (in m)?
2. 2.What is the smallest whole number by which 240 must be divided to get a perfect square?
3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 90²? =
6. 6.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 350 must be divided to get a perfect square?
10. 10.A square garden has an area of 3136 square m. How long is each side (in m)?
11. 11.What is 52²? =
12. 12.Which of these is a perfect square? (a) 1600 (b) 1653 (c) 1626
13. 13.Which of these is a perfect square? (a) 1364 (b) 1322 (c) 1296
14. 14.Which of these is a perfect square? (a) 189 (b) 172 (c) 169
15. 15.What is √8464? =
16. 16.What is √2025? =
17. 17.A square garden has an area of 144 square m. How long is each side (in m)?
18. 18.A square garden has an area of 400 square m. How long is each side (in m)?
19. 19.What is 63²? =
20. 20.A square garden has an area of 36 square m. How long is each side (in m)?
21. 21.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 63 must be divided to get a perfect square?
23. 23.What is the smallest whole number by which 50 must be divided to get a perfect square?
24. 24.Which of these is a perfect square? (a) 328 (b) 325 (c) 324
25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
26. 26.Which of these is a perfect square? (a) 256 (b) 265 (c) 257
27. 27.What is √576? =
28. 28.A square garden has an area of 361 square m. How long is each side (in m)?
29. 29.A square garden has an area of 1936 square m. How long is each side (in m)?
30. 30.What is √3136? =
31. 31.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
32. 32.A square garden has an area of 576 square m. How long is each side (in m)?
33. 33.What is 48²? =
34. 34.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
35. 35.What is 29²? =
36. 36.What is 69²? =
37. 37.What is the smallest whole number by which 405 must be divided to get a perfect square?
38. 38.What is 93²? =
39. 39.What is 19²? =
40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

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