Question

which two numbers does the square root of 128 lie between on a number line

Answer 1

1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9²=81
10²=100
11²=121
12²=144

128 is between 121 and 144.
Thus, the square root of 128 must be between the square root of 121 and the square root of 144.
Thus, the square root of 128 is between 11 and 12. You can check this for yourself by using a calculator.

Answer 2

√121 = 11
√144 = 12

Since √128 is between √121 and √144,
then its square root is between 11 and 12.