Final answer:
The true inequalities are: 0 < square root of 8, square root of 8 < 3, and square root of 8 > square root of 7. The square root of 8 < 2 and the square root of 8 > 8 are false. The true statements reflect the relations between square roots and other numbers based on their values.
Step-by-step explanation:
To determine which inequalities are true, we need to evaluate the relationships between the square roots and other numbers presented. Let's examine each inequality:
- 0 < square root of 8: Since the square root of any positive number is positive, this inequality is true.
- Square root of 8 < 3: The square root of 8 is approximately 2.83, which is less than 3, making this inequality true.
- Square root of 8 > square root of 7: Since 8 is greater than 7, and both numbers are positive, their square roots will also maintain this order. This inequality is true.
- Square root of 8 < 2: Since 2 squared is 4 and 4 is less than 8, the square root of 8 must be greater than 2. This inequality is false.
- Square root of 8 > 8: The square root of 8 is less than 8 because the square root of a number less than its square is always less than the original number. This inequality is false.
- 1 < square root of 8: This is true because the square root of 8 is greater than 1 since 8 is greater than 1 squared.
By analyzing the square roots and applying properties of inequalities, we can conclude which statements are true or false based on the numerical values and relationships.