Volume · Usually met around P5
Square roots and cube roots
√: which number times itself? ∛: times itself three times?
How to do it
Method
√: which number times itself? ∛: times itself three times?
√49 = 7, ∛64 = 4
Another way
Picture a square and a cube
A square of area 49 has side 7
In full
A number times itself makes a square number: 7 × 7 = 49. Ask it backwards, “which number times itself makes 49?”, and the answer 7 is the square root of 49, written √49 = 7: a square of area 49 cm² has 7 cm sides. In the same way 4 × 4 × 4 = 64, so the cube root of 64 is 4, written ∛64 = 4: a cube of volume 64 cm³ has 4 cm edges. Way 1: know the square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and the cube numbers 1, 8, 27, 64, 125. Way 2: try numbers in turn: 3 × 3 × 3 = 27 is too small, 4 × 4 × 4 = 64 is just right. Check: multiply the answer by itself twice (or three times) and you get the number back; squaring and square-rooting undo each other. A number that isn't square has its square root between two whole numbers next to each other: 49 < 50 < 64, so √50 is between 7 and 8.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
√1 = □
Show the answer and working
Answer: 1
Which number times itself makes 1? 1 × 1 = 1, so √1 = 1.
Example 2
What does “√64 = 8” mean?
- A. 8 times itself three times makes 64
- B. Half of 64 is 8
- C. 8 times 2 makes 64
- D. 8 times itself makes 64
Choose the right answer
Show the answer and working
Answer: D. 8 times itself makes 64
√64 asks which number times itself makes 64: 8 × 8 = 64.
Example 3
√20 lies between two whole numbers next to each other. What is the smaller one?
Show the answer and working
Answer: 4
4 × 4 = 16 and 5 × 5 = 25; 16 < 20 < 25, so √20 is between 4 and 5.
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