Which of the following results in a sum or a product that is rational. select all that apply.
a.3.12repeating x 1.4 ***
b. power symbol 9 x power symbol 25
c. to the power symbol 2 x power symbol 3
d. 4+5***
e. pi x 3
To determine which of the following options results in a rational sum or product, we need to understand what rational numbers are. Rational numbers are numbers that can be expressed as the ratio of two integers (where the denominator is not zero).
Let's analyze each option one by one:
a. 3.12repeating x 1.4:
For this option, we have two decimal numbers being multiplied. Decimal numbers can be rational or irrational. However, if we multiply a rational number by another rational number, the result is always rational. Therefore, this option results in a rational product.
b. Power symbol 9 x Power symbol 25:
Without knowing the values inside the power symbols, it is not possible to determine the nature of the result. We need to know the numbers being raised to powers to make a conclusion.
c. To the power symbol 2 x Power symbol 3:
Similar to option b, we need to know the specific numbers being raised to powers to determine if the result is rational or not.
d. 4 + 5:
This option involves a simple addition operation between two integers. Adding integers always results in another integer, which is a rational number.
e. Pi x 3:
Pi (π) is an irrational number, meaning it cannot be expressed as a ratio of two integers. When we multiply an irrational number with any other number, the result is always irrational.
In summary, the options that result in a sum or product that is rational are:
- Option a: 3.12repeating x 1.4
- Option d: 4 + 5