Multiplying and dividing by two digits; divisibility · Usually met around P4
Square and cube numbers
²: two of it multiplied; ³: three.
How to do it
Method
²: two of it multiplied; ³: three
4³ = 4 × 4 × 4 = 64
Another way
Square, then once more
4³ = 4² × 4 = 16 × 4 = 64
In full
A number times itself makes a square number, written 5² and read “5 squared”: 5² = 5 × 5 = 25. Three equal numbers multiplied make a cube number, written 4³ and read “4 cubed”: 4³ = 4 × 4 × 4 = 64. Careful: 5² is not 5 × 2, and 4³ is not 4 × 3. From 1 to 125 there are only five cube numbers: 1, 8, 27, 64 and 125. Square numbers make squares of dots and cube numbers make cubes of blocks: 3³ is a cube 3 blocks along each edge, 3 × 3 = 9 blocks a layer and 3 layers, 27 in all. Or work out a cube in two steps, the square first and then one more multiplication: 4³ = 4² × 4 = 16 × 4 = 64.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Work out: 10³ = □
Show the answer and working
Answer: 1000
10³ is three 10s multiplied: 10 × 10 = 100, then 100 × 10 = 1000.
Example 2
What does 11² mean?
- A. 11 × 2
- B. 11 × 11 × 11
- C. 11 + 11
- D. 11 × 11
Choose the right answer
Show the answer and working
Answer: D. 11 × 11
11² is read “11 squared”: two 11s multiplied, 11 × 11.
Example 3
□² = 49
Show the answer and working
Answer: 7
Find the number that times itself makes 49: 7 × 7 = 49.
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