To find all possible values of each expression using the given inequalities, we need to consider the range of values that the square roots of 2 (√2) and 3 (√3) can take based on the provided inequalities.
1. For the expression √√2:
- From the inequality 1.4 < √√2 < 1.5, we can square both sides to find possible values for √2.
- Squaring the inequality gives 1.96 < √2 < 2.25.
- Then, taking the square root gives 1.4 < √2 < 1.5.
- Finally, taking the square root again gives 1.1832 < √√2 < 1.2247 as the possible values for √√2.
2. For the expression √3:
- From the inequality 1.7 < √3 < 1.8, we can square both sides to find possible values for √3.
- Squaring the inequality gives 2.89 < 3 < 3.24.
- Then, taking the square root gives 1.7 < √3 < 1.8 as the possible values for √3.
Therefore, the possible values of each expression are:
- For √√2: 1.1832 < √√2 < 1.2247
- For √3: 1.7 < √3 < 1.8
These ranges represent all the values that satisfy the given inequalities for each expression.
