Question

If the square of a number is less than 1, does it follow that the number must be less than 1? If the square of a positive number is greater than 1, does it follow that the number must be greater than 1? Include examples to explain your reasoning.​

Answer 1

1.

Yes.  If x^2 < 1, then x < 1.

examples: (0.5)^2 = 0.25, (0.9)^2 = 0.81

2.

Yes.  If x^2 > 1, then x > 1.

examples 3^2 = 9,  1.1^2 = 1.21

Any positive number mutiplied by a number greater than 1 will grow.  So if both numbers are greater than 1, the result will be larger than either original number, which will be greater than 1.

Any positive number mutiplied by a number less than 1 will shrink.  So if both numbers are less than 1, the result will be smaller than either original number, which will still be less than 1.