Question

color in each square in the grid below that contains a perfect square.
102 95 115 11 40 121 361 222 8 135
75 17 24 99 30 1 25 169 37 82
150 50 15 33 80 225 35 16 324 3
5 98 63 95 70 256 84 70 36 120
111 15 300 10 20 1 20 110 196 60
45 14 50 140 12 4 145 40 4 37
55 90 48 40 80 16 95 49 2 85
105 98 49 144 25 289 60 96 26 90
13 400 9 36 64 9 45 75 35 5
101 35 81 100 64 10 35 65 65 82

Explanation:

Step1: Recall perfect square definition

A perfect square is a number \( n = k^2 \), where \( k \) is an integer. We check each number:

Step2: Check row 1

• \( 121 = 11^2 \), \( 361 = 19^2 \) → color these.

Step3: Check row 2

• \( 1 = 1^2 \), \( 25 = 5^2 \), \( 169 = 13^2 \) → color these.

Step4: Check row 3

• \( 225 = 15^2 \), \( 16 = 4^2 \), \( 324 = 18^2 \) → color these.

Step5: Check row 4

• \( 256 = 16^2 \), \( 36 = 6^2 \) → color these.

Step6: Check row 5

• \( 1 = 1^2 \), \( 196 = 14^2 \) → color these.

Step7: Check row 6

• \( 4 = 2^2 \), \( 4 = 2^2 \) → color these.

Step8: Check row 7

• \( 16 = 4^2 \), \( 49 = 7^2 \) → color these.

Step9: Check row 8

• \( 49 = 7^2 \), \( 144 = 12^2 \), \( 25 = 5^2 \), \( 289 = 17^2 \) → color these.

Step10: Check row 9

• \( 400 = 20^2 \), \( 9 = 3^2 \), \( 36 = 6^2 \), \( 64 = 8^2 \), \( 9 = 3^2 \) → color these.

Step11: Check row 10

• \( 81 = 9^2 \), \( 100 = 10^2 \), \( 64 = 8^2 \) → color these.

(Full list of perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400)

Answer:

Color the squares with numbers: 121, 361, 1, 25, 169, 225, 16, 324, 256, 36, 1, 196, 4, 4, 16, 49, 49, 144, 25, 289, 400, 9, 36, 64, 9, 81, 100, 64. (Visual: Locate each number and color its square.)