Final answer:
The irrational numbers from the given options are square root of 10, square root of 27, and square root of 99 because these numbers are not perfect squares and their square roots cannot be expressed as simple fractions.
Step-by-step explanation:
When selecting irrational numbers from a given list, it's important to understand the difference between rational and irrational numbers. A rational number can be expressed as a fraction with both the numerator and the denominator as integers, while an irrational number cannot be expressed in this way and it has non-terminating, non-repeating decimal expansions.
Let's consider each of the given numbers:
- √10 (square root of 10): This is an irrational number because 10 is not a perfect square and its square root cannot be expressed as a simple fraction.
- √27 (square root of 27): Like √10, this is also an irrational number for the same reason.
- √49 (square root of 49): This is not an irrational number; it is rational because 49 is a perfect square and its square root is 7, an integer.
- √64 (square root of 64): This is also not an irrational number as 64 is a perfect square, with its square root being 8, an integer as well.
- √99 (square root of 99): This is an irrational number because 99 is not a perfect square and its square root cannot be neatly expressed as a fraction.
Therefore, the irrational numbers from the given options are square root of 10, square root of 27, and square root of 99.