Question

complete the table below.

length	1		3		5	6		8		10		12
perfect square	1	4		16		36	49		81		121

Explanation:

Step1: Identify the pattern (perfect squares)

A perfect square of a number \( n \) is \( n^2 \). So for length \( n \), perfect square is \( n^2 \).

Step2: Fill in missing lengths

• For perfect square 4: \( n^2 = 4 \Rightarrow n = 2 \) (since \( 2^2 = 4 \))
• For length 3: \( n = 3 \Rightarrow 3^2 = 9 \)
• For perfect square 16: \( n^2 = 16 \Rightarrow n = 4 \) (since \( 4^2 = 16 \))
• For length 5: \( n = 5 \Rightarrow 5^2 = 25 \)
• For perfect square 49: \( n^2 = 49 \Rightarrow n = 7 \) (since \( 7^2 = 49 \))
• For length 8: \( n = 8 \Rightarrow 8^2 = 64 \)
• For perfect square 81: \( n^2 = 81 \Rightarrow n = 9 \) (since \( 9^2 = 81 \))
• For length 10: \( n = 10 \Rightarrow 10^2 = 100 \)
• For perfect square 121: \( n^2 = 121 \Rightarrow n = 11 \) (since \( 11^2 = 121 \))
• For length 12: \( n = 12 \Rightarrow 12^2 = 144 \)

Answer:

Length	1	2	3	4	5	6	7	8	9	10	11	12