Which of the following is a rational number: 32−−√, 81−−√, 90−−√, or 125−−−√?(1 point)
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are integers.
In this case, 81 and 125 can be expressed as perfect squares (81 = 9^2 and 125 = 5^3), so their square roots are rational numbers.
Therefore, the rational numbers in the given options are 81^-1/2 and 125^-1/3.
The correct answer is 81−−√.
To determine which of the given numbers is a rational number, we need to check if the number can be written as a fraction, where both the numerator and denominator are integers.
Let's go through each option:
1. 32−−√: This number cannot be simplified further, so it is not a rational number.
2. 81−−√: This number is equal to 9, which can be written as 9/1. Both the numerator and denominator are integers, so 81−−√ is a rational number.
3. 90−−√: This number cannot be simplified further, so it is not a rational number.
4. 125−−−√: This number cannot be simplified further, so it is not a rational number.
Therefore, the only rational number among the options is 81−−√.