Which of the following is a rational number: 32−−√, 81−−√, 90−−√, or 125−−−√?
Remember that a rational number is a number that can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are both integers and $b \neq 0$. The only number that can be expressed in this form is $\boxed{81-\sqrt{}}$, since it is equal to $9 = \frac{9}{1}$.
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Which of the following is a rational number: 32−−√, 81−−√, 90−−√, or 125−−−√?
To determine which of the following numbers is rational, we need to identify if any of them can be expressed as a ratio of two integers.
Let's check each option:
1. √32 is an irrational number since it cannot be simplified as a fraction or expressed as the quotient of two integers.
2. √81 = 9, which can be expressed as the ratio 9/1. Therefore, 81−−√ is a rational number.
3. √90 is an irrational number since it cannot be simplified as a fraction or expressed as the quotient of two integers.
4. √125 is an irrational number since it cannot be simplified as a fraction or expressed as the quotient of two integers.
So, the only rational number among the given options is 81−−√.