Estimating Square Roots - Practice

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 23

• 25

• 16

• 36

Answer explanation

To find the closest perfect square to 23, we compare the squares of integers: 4²=16, 5²=25, and 6²=36. The differences are |23-16|=7, |23-25|=2, and |23-36|=13. The smallest difference is with 25, making it the closest perfect square.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 129

• 121

• 144

• 100

Answer explanation

To find the closest perfect square to 129, we check the squares of integers around its square root (approximately 11.36). The perfect squares are 121 (11^2) and 144 (12^2). 125 is not a perfect square, but it's the closest number to 129.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 91

• 81

• 100

• 121

Answer explanation

To find the closest perfect square to 91, we compare the squares of integers around the square root of 91, which is approximately 9.54. The perfect squares are 81 (9^2) and 100 (10^2). 100 is closer to 91 than 81.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 115

• 100

• 121

• 144

Answer explanation

To find the closest perfect square to 115, we compare the squares of integers around the square root of 115, which is approximately 10.72. The perfect squares are 100 (10^2) and 121 (11^2). 121 is closer to 115 than 100.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 385

• 361

• 400

• 441

Answer explanation

To find the closest perfect square to 385, we check the squares of integers around its square root (approximately 19.6). The perfect squares are 361 (19^2) and 400 (20^2). 400 is closer to 385 than 361, making it the correct choice.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 75

• 64

• 81

• 49

• 76

Answer explanation

To find the closest perfect square to 75, we compare the squares of integers. 8^2 = 64 and 9^2 = 81. The difference from 75 is smaller for 64 (11) than for 81 (6). Thus, the closest perfect square is 64.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 186

• 169

• 196

• 225

• 182

Answer explanation

To find the closest perfect square to 186, we compare the squares of integers around the square root of 186, which is approximately 13.6. The perfect squares are 169 (13^2) and 196 (14^2). Since 186 is closer to 196, the correct answer is 196.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 57

• 49

• 64

• 36

• 52

Answer explanation

To find the closest perfect square to 57, we compare the squares of integers. 7^2 = 49 and 8^2 = 64. The difference between 57 and 49 is 8, while the difference between 57 and 64 is 7. Thus, 49 is the closest perfect square.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 228

• 225

• 256

• 196

• 232

Answer explanation

To find the closest perfect square to 228, we compare the squares of integers around the square root of 228, which is approximately 15.1. The perfect squares are 225 (15^2) and 256 (16^2). 225 is closer to 228 than 256.

Given each of the following non-perfect squares, find the Perfect Square that is closest to it: 391

• 361

• 400

• 441

• 382

Answer explanation

To find the closest perfect square to 391, we compare the squares of integers around its square root (approximately 19.8). The perfect squares are 361 (19^2), 400 (20^2), and 441 (21^2). 400 is closest to 391.