True or False: Are these numbers rational?(1 point)
The numbers are: 8, -9.345, square root 15, and square root 81.
True
Which ones are true?
The numbers 8 and square root 81 are rational.
What about -9.345 and square root 15? Are those two rational as well?
No, -9.345 and square root 15 are not rational numbers.
To determine whether these numbers are rational or not, we need to understand what rational numbers are.
Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. They can be written in the form of p/q, where p and q are integers, and q is not equal to zero.
Let's analyze the given numbers one by one:
1. 8: 8 can be written as the fraction 8/1, where both 8 and 1 are integers. Therefore, 8 is a rational number.
2. -9.345: -9.345 is a decimal number. Decimal numbers can be rational or irrational. To determine if it is rational, we need to check if it can be expressed as a fraction. In this case, -9.345 cannot be expressed as a fraction of two integers. Hence, -9.345 is an irrational number.
3. Square root of 15: The square root of 15 (√15) is an example of an irrational number. Irrational numbers are numbers that cannot be expressed as a fraction of two integers. The square root of 15 is an irrational number because it cannot be expressed without a radical sign.
4. Square root of 81: The square root of 81 (√81) is a rational number. The square root of 81 equals 9, which is an integer. Therefore, √81 can be written as the fraction 9/1, where both 9 and 1 are integers. Hence, √81 is a rational number.
In summary:
- 8 is a rational number.
- -9.345 is an irrational number.
- √15 is an irrational number.
- √81 is a rational number.
So, there is a mixture of rational and irrational numbers among the given numbers.