New
New
Year 7

Square and cube roots

I can explain the concept of square root and cube root and calculate them.

New
New
Year 7

Square and cube roots

I can explain the concept of square root and cube root and calculate them.

Lesson details

Key learning points

  1. The square root of any perfect square will be an integer.
  2. The square root of any perfect square will be an integer and can be calculated by using trial and improvement.
  3. The cube root of any perfect cube will be an integer.
  4. The cube root of any perfect cube will be an integer and can be calculated by using trial and improvement.

Common misconception

The root of an integer is half of the integer.

The square root is the inverse of a square number. A square is the product of 2 repeated integers.

Keywords

  • Perfect square - A perfect square is the same as a square number.

  • Perfect cube - A perfect cube is the same as a cube number.

  • Square number - A square number is the product of two repeated integers.

  • Cube number - A cube number is the product of three repeated integers.

Maybe, introduce the title of the lesson and allow students to work with manipulatives to see what prior knowledge they have. Weaker students will benefit from being able to physically rearrange them and it should help with the misconception.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Which of the following are square numbers?
Correct answer: 1
2
3
Correct answer: 4
5
Q2.
Which of the following is a cube number?
2
4
6
Correct answer: 8
10
Q3.
Match the descriptions to the correct list of numbers.
Correct Answer:square numbers,1, 4, 9, 16, 25, 36, ...

1, 4, 9, 16, 25, 36, ...

Correct Answer:cube numbers,1, 8, 27, 64, 125, 216, ...

1, 8, 27, 64, 125, 216, ...

Correct Answer:even numbers,2, 4, 6, 8, 10, 12, ...

2, 4, 6, 8, 10, 12, ...

Correct Answer:odd numbers,1, 3, 5, 7, 9, 11, ...

1, 3, 5, 7, 9, 11, ...

Correct Answer:multiples of 3,3, 6, 9, 12, 15, 18, ...

3, 6, 9, 12, 15, 18, ...

Correct Answer:multiples of 1,1, 2, 3, 4, 5, 6, ...

1, 2, 3, 4, 5, 6, ...

Q4.
Which of the following is a perfect square?
11
111
Correct answer: 121
131
141
Q5.
Work out the sum of the square of 4 and the cube of 4
16
18
32
Correct answer: 80
100
Q6.
Some students are talking about square numbers. Who is correct?
Jun says, "There are only 2 square numbers which are also cube numbers: 1 & 64."
Aisha says, "There are no square numbers which are also cube numbers."
Jacob says, "Every number is a square number and cube number."
Correct answer: Sam says, "There's an infinite number of square numbers that are cube numbers."

6 Questions

Q1.
An array is a perfect square and has 256 dots. What is the row and column length of the array?
4
8
Correct answer: 16
128
256
Q2.
Work out $$\sqrt{100}$$
1
Correct answer: 10
100
1000
10 000
Q3.
Work out $$\sqrt[3]{125}$$
Correct answer: 5
25
62.5
15 625
Q4.
Match each calculation to its correct answer.
Correct Answer: $$\sqrt{64}$$,8

8

Correct Answer: $$\sqrt[3]{125}$$,5

5

Correct Answer:$$\sqrt{1}$$,1

1

Correct Answer:$$\sqrt{49}$$,7

7

Correct Answer:$$\sqrt{169}$$,13

13

Correct Answer: $$\sqrt[3]{64}$$,4

4

Q5.
Find the closest integer to $$\sqrt{40}$$
4
5
Correct answer: 6
7
Q6.
Find the closest integer to $$\sqrt[3]{1600}$$
9
10
11
Correct answer: 12
13