Last reviewed: 7 November 2026
Updated November 2026. These Grade 9 cubes and cube roots notes explain how to find the cube of a number, how to find a cube root by the factor method, and when to use mathematical tables or a calculator. The cube of a number is the number multiplied by itself three times: 4³ = 4 × 4 × 4 = 64. The cube root reverses this: ∛64 = 4, because 4 × 4 × 4 = 64.
The examples and questions below are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
Cubes and cube roots is a sub-strand under Numbers in the Grade 9 Mathematics design published by the Kenya Institute of Curriculum Development. Learners work out cubes by multiplication, from mathematical tables and with a calculator, find cube roots by the factor method, tables and calculator, and apply both in real-life situations such as the volume of a cube. The design is listed on the KICD Grade Nine curriculum designs page.
Cubes of Numbers by Multiplication
Cubing is a power with index 3, so the laws of indices apply, as shown in OpenStax Prealgebra’s section on properties of exponents. Learning the first cubes by heart saves time in tests.
| n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| n³ | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 | 1,000 |
Cubes of decimals and fractions
- 0.2³ = 0.2 × 0.2 × 0.2 = 0.008. Count decimal places: each 0.2 has one, so the answer has three.
- (2/3)³ = (2 × 2 × 2) ÷ (3 × 3 × 3) = 8/27. Cube the numerator and the denominator separately.
- (−3)³ = −27. A negative number cubed stays negative, because there are three negative signs.
A frequent mistake is writing 0.2³ = 0.8. Multiplying three decimals makes the number much smaller, not bigger.
Cube Roots by the Factor Method
To find a cube root without a calculator, write the number as a product of prime factors, group the factors in threes, and take one factor from each group.
Worked example: find ∛2,744
- Prime factors: 2,744 = 2 × 2 × 2 × 7 × 7 × 7.
- Group in threes: (2 × 2 × 2) × (7 × 7 × 7) = 2³ × 7³.
- Take one from each group: 2 × 7 = 14.
- Check: 14 × 14 × 14 = 2,744. Correct.
Worked example: find ∛9,261
9,261 = 3 × 3 × 3 × 7 × 7 × 7 = 3³ × 7³. So ∛9,261 = 3 × 7 = 21. If the factors do not group neatly into threes, the number is not a perfect cube and you will need tables or a calculator.
Cube roots of fractions and decimals
∛(27/64) = ∛27 ÷ ∛64 = 3/4. For a decimal, change to a fraction first: 0.125 = 125/1,000, so ∛0.125 = 5/10 = 0.5.
Using Tables and Calculators
Mathematical tables list cubes (and in some books cube roots) for numbers between 1 and 10, often to four figures. For a number outside that range, write it in standard form first and adjust the decimal point. On a calculator, use the x³ key for cubes and the ∛ key (often a second-function key) for cube roots. Your teacher will say which method a test allows, so practise all three. Always check a calculator answer by cubing it back.
Real-Life Uses
The volume of a cube is side × side × side, so cubes and cube roots appear whenever a container or box has equal sides. In this made-up example, a cube-shaped water tank holds 3.375 m³. Its side is ∛3.375 = 1.5 m, which tells a fundi how much space to leave on a stand. Going the other way, a cube-shaped box of side 40 cm has a volume of 40³ = 64,000 cm³. For more on volume, see our volume and capacity notes.
Original Practice Questions With Worked Answers
- Evaluate 12³. 12 × 12 = 144; 144 × 12 = 1,728.
- Find ∛1,728 by the factor method. 1,728 = 2⁶ × 3³ = (2 × 2 × 3)³ = 12³, so ∛1,728 = 12.
- Evaluate (−0.3)³. 0.3 × 0.3 × 0.3 = 0.027; three negatives give −0.027.
- Find ∛(8/125). ∛8 ÷ ∛125 = 2/5.
- A cube has a volume of 343 cm³. Find the length of one edge. ∛343 = 7 cm.
- Is 500 a perfect cube? 500 = 2 × 2 × 5 × 5 × 5. The two 2s do not make a group of three, so no.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the difference between a cube and a cube root?
The cube of a number is the number multiplied by itself three times. The cube root is the number that, multiplied by itself three times, gives the original number. For example, 5³ = 125 and ∛125 = 5.
How do you find a cube root without a calculator?
Use the factor method: write the number as prime factors, group identical factors in threes, and multiply one factor from each group.
Can a negative number have a cube root?
Yes. ∛(−8) = −2, because (−2) × (−2) × (−2) = −8.
Where are cube roots used in real life?
They are used to find the side length of cube-shaped objects such as boxes and tanks when the volume is known.