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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

1. Observe the pattern and find the next square number by drawing and counting dots in the
given box.

1 4 9 16 25 —
2. Find the area of a square with the given side length.
(a) 3 cm (b) 11 m (c) 8 mm (d) 100 m
3. Fill in the blanks.
2
2

(a) (100 + 5) = ............... (b) (121) = ...............
4. Observe the pattern given below and write the next two rows.
2
6 = 36
2
66 = 4356
666 = 443556
2
2
6666 = 44435556
………........... = ………………..
………........... = ………………..

Square Numbers

We know that a square has equal sides and the area of a square = side × side (where
‘side’ means ‘the length of a side’). Observe the following table.
Side
2
Side of a square (in cm) Area of the square (in cm )
2
1 1 × 1 = 1 = 1 Side
2
2 2 × 2 = 2 = 4
2
3 3 × 3 = 3 = 9
2
4 4 × 4 = 4 = 16
5 5 × 5 = 5 = 25 Square
2
2
6 6 × 6 = 6 = 36 2 = 2 × 2 = 4 (Square number)
2
7 7 × 7 = 7 = 49
2
2
8 8 × 8 = 8 = 64
M M
a a × a = a 2

Clearly, 1 is the square of 1, 4 is the square of 2, 9 is the square of 3, 16 is the square of 4 and 25
2
is the square of 5. So, 1, 4, 9, 16 and 25 are called square numbers. The expression 1 (read as ‘1
raised to the power 2’) means 1 is multiplied by itself 2 times, 2 (read as ‘2 raised to the power 2’)
2
2
means 2 is multiplied by itself 2 times, 3 (read as ‘3 raised to the power 2’) means 3 is multiplied
by itself 2 times, and so on.

So, when a number is raised to the power of 2 or the exponent is 2, the result is a square (number).

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