Question

Determining bounds for square root approximations plot √0.9 on the number line. Which inequalities are true? Check all that apply.

1) 0 < √0.9 < 0.9
2) √0.9 < 1
3) √0.9 > √1
4) 0.9 > √0.9 < 1

Answer 1

The square root of 0.9 is less than 0.9 and less than 1. The true inequalities are 0 < √0.9 < 0.9, √0.9 < 1, and 0.9 > √0.9 < 1.

Step-by-step explanation:

To determine the bounds for square root approximations and plot √0.9 on the number line, we need to consider which inequalities are true. We know that the square root of a number is less than or equal to the number itself if the number is positive. Thus, since 0.9 is positive, 0.9 > √0.9. Furthermore, we know that the square root of 1 is 1, and since 0.9 is less than 1, it follows that √0.9 < 1. Additionally, since 1 is the square root of 1, √0.9 cannot be greater than √1. So the correct inequalities are 0 < √0.9 < 0.9, √0.9 < 1, and 0.9 > √0.9 < 1.

=