Year 6 Maths: Square Roots

What are Square Roots?

Hello, Year 6! Today, we are going to learn about square roots. A square root is a special number that tells us what number was multiplied by itself to get another number.

Understanding Square Roots

Let’s break it down:

• The square root of a number n is a number x such that when you multiply x by itself (or square it), you get n.
• We write this as: $$ \sqrt{n} = x $$

For example, if we take the number 9:

• The square root of 9 is 3 because $$ 3 \times 3 = 9 $$.
• So, we can say $$ \sqrt{9} = 3 $$.

Key Rules About Square Roots

1. Perfect Squares: Numbers like 1, 4, 9, 16, 25, and 36 are called perfect squares because they have whole number square roots.
   • Example: $$ \sqrt{16} = 4 $$ because $$ 4 \times 4 = 16 $$.
2. Zero: The square root of 0 is 0.
   • $$ \sqrt{0} = 0 $$ because $$ 0 \times 0 = 0 $$.
3. Negative Numbers: We cannot find the square root of negative numbers in the set of real numbers.
   • Example: $$ \sqrt{-1} $$ does not have a real answer.

Tips and Tricks

• Use a Square Numbers Chart: Create a chart of perfect squares from 1 to 12. This will help you remember the square roots.
• Practice: The more you practice, the better you’ll get at finding square roots!
• Visualize with Squares: Imagine drawing squares. If you have 9 tiles arranged in a perfect square (like 3 tiles by 3 tiles), you can see that 3 is the square root of 9.

Examples of Square Roots

• $$ \sqrt{1} = 1 $$
• $$ \sqrt{4} = 2 $$
• $$ \sqrt{25} = 5 $$
• $$ \sqrt{36} = 6 $$

Now, let’s practice! Here are some questions for you to try.

Questions

Easy Level (Questions 1-20)

1. What is $$ \sqrt{1} $$?
2. What is $$ \sqrt{4} $$?
3. What is $$ \sqrt{9} $$?
4. What is $$ \sqrt{16} $$?
5. What is $$ \sqrt{25} $$?
6. What is $$ \sqrt{36} $$?
7. What is $$ \sqrt{49} $$?
8. What is $$ \sqrt{64} $$?
9. What is $$ \sqrt{81} $$?
10. What is $$ \sqrt{100} $$?
11. What is $$ \sqrt{0} $$?
12. What is the square root of 16 using a calculator?
13. What whole number squared gives 25?
14. What is the square root of 1?
15. What is $$ \sqrt{64} $$?
16. How many tiles form a square of 9?
17. Find the square root of 36.
18. What is $$ \sqrt{121} $$?
19. What is $$ \sqrt{144} $$?
20. What is the square root of 49?

Medium Level (Questions 21-40)

21. What is $$ \sqrt{256} $$?
22. If $$ x^2 = 64 $$, what is $$ x $$?
23. What is the square root of 225?
24. What is $$ \sqrt{400} $$?
25. Find the square root of 144.
26. If $$ x = 8 $$, what is $$ \sqrt{x^2} $$?
27. What is $$ \sqrt{121} $$?
28. What number squared gives 36?
29. What is $$ \sqrt{484} $$?
30. Find the square root of 196.
31. If the area of a square is 81, what is the length of one side?
32. What is $$ \sqrt{500} $$ rounded to the nearest whole number?
33. If $$ x^2 = 49 $$, what are the possible values for $$ x $$?
34. Calculate $$ \sqrt{729} $$.
35. What is the square root of 1000 rounded down?
36. What is $$ \sqrt{1024} $$?
37. Find the square root of 169.
38. If the side of a square is 10, what is its area?
39. What number squared equals 121?
40. What is $$ \sqrt{361} $$?

Hard Level (Questions 41-60)

41. Calculate $$ \sqrt{625} $$.
42. What is the square root of 289?
43. If $$ x^2 = 144 $$, what are the values for $$ x $$?
44. Find $$ \sqrt{729} $$ and explain each step.
45. If a square has a perimeter of 40 cm, what is the length of one side?
46. What is the square root of 196?
47. If the area of a square is 256 cm², what is the length of a side?
48. Find the square root of 361.
49. What is $$ \sqrt{324} $$?
50. If $$ x^2 = 225 $$, what are the values for $$ x $$?
51. What is the square root of 484?
52. How would you find $$ \sqrt{625} $$ without a calculator?
53. Calculate $$ \sqrt{49} $$ and explain your reasoning.
54. If a square has an area of 121 cm², what is the length of the side?
55. What is $$ \sqrt{144} $$?
56. If $$ x^2 = 16 $$, what is $$ x $$?
57. Find the square root of 900.
58. If the side of a square is 12, what is its area?
59. What is the square root of 10000?
60. What is $$ \sqrt{256} $$?

Answers

Easy Level Answers

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6
7. 7
8. 8
9. 9
10. 10
11. 0
12. 4
13. 5
14. 1
15. 8
16. 3
17. 6
18. 11
19. 12
20. 7

Medium Level Answers

21. 16
22. 8
23. 15
24. 20
25. 12
26. 8
27. 11
28. 6
29. 22
30. 14
31. 9
32. 22
33. 7 and -7
34. 27
35. 31
36. 32
37. 13
38. 100
39. 11
40. 19

Hard Level Answers

41. 25
42. 17
43. 12 and -12
44. 27 (27 x 27 = 729)
45. 10 cm
46. 14
47. 16 cm
48. 19
49. 18
50. 15 and -15
51. 22
52. 25 (25 x 25 = 625)
53. 7 (7 x 7 = 49)
54. 11 cm
55. 12
56. 4 and -4
57. 30
58. 144
59. 100
60. 16

I hope this helps you understand square roots better! Keep practicing, and soon it will be a piece of cake!