Estimating Square Roots - Practice

Front

Find the Perfect Square closest to 23.

Back

25

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.

Front

Find the Perfect Square closest to 129: 121, 144, 100

Back

121

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.

Front

Find the Perfect Square closest to 91: 81, 100, 121

Back

100

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.

Front

Find the Perfect Square closest to 115.

Back

121

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.

Front

Find the Perfect Square closest to 385: 361, 400, 441

Back

400

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.

Front

Find the Perfect Square closest to 75. Options: 64, 81, 49, 76.

Back

64

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.

Front

Find the Perfect Square closest to 186: 169, 196, 225, 182

Back

196

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.

Front

Find the Perfect Square closest to 57: 49, 64, 36, 52

Back

49

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.

Front

Find the Perfect Square closest to 228: 225, 256, 196, 232

Back

225

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.

Front

Find the Perfect Square closest to 391: 361, 400, 441, 382

Back

400

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.