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1. Observe the given pattern and extend it up to the next two steps.
............... ...............
1 1 + 7 = 8 1 + 7 + 19 = 27
2. Observe the given pattern and fill in the next 3 numbers.
1, 8, 27, 64, 125, ..............., ..............., ...............
3. Find the value of the following:
(a) 4 3 (b) 10 3 (c) 1 3
5
Cubes
We are already familiar with the term ‘Cube’ in geometry. It is a 3-dimensional solid figures whose
all sides are equal, i.e., its length, breadth and height are all
the same.
Think and Answer
How many cubes of side 2 cm will
make a cube of side 8 cm?
Cube of side 1 cm Cube of side 2(1 + 1) cm Cube of side 3 (1 + 1 + 1) cm
We know that when we multiply a number by itself we get a square number. Similarly, when a
number is multiplied by itself 3 times, the product obtained is called the cube of that number.
Cube of a number is also called “raised to the power 3”.
For example:
3
3
(a) 3 × 3 × 3 = 27 = 3 ⇒ 3 or 27 is the cube of 3. Cube or “raised to the power 3’’
3
3
(b) 4 × 4 × 4 = 64 = 4 ⇒ 4 or 64 is the cube of 4. ↓
3
2 = 8
3
3
(c) 11 × 11 × 11 = 1331 = 11 ⇒ 11 or 1331 is the cube of 11.
3
Thus, if x is any number, then the cube of x is x .
The following table gives the cubes of the first 10 natural numbers.
Natural number 1 2 3 4 5 6 7 8 9 10
Cube 1 8 27 64 125 216 343 512 729 1000
Cubes of Negative Integers
Cubes of positive integers are always positive integers, while the cubes of negative integers are
always negative integers.
3
For example: (a) (–2) = (–2) × (–2) × (–2) = –8 (b) (–5) = (–5) × (–5) × (–5) = –125
3
Cubes of Decimals
Like integers, the cube of a decimal number can be obtained by multiplying the decimal number
by itself thrice.
3
3
For example: (a) (2.5) = (2.5) × (2.5) × (2.5) = 15.625 (b) (–1.1) = (–1.1) × (–1.1) × (–1.1) = –1.331
149 Cubes and Cube Roots
