Which of the following results in a sum or a product that is rational? Choose all that apply.
(2 points)
Responses
a. 3.12 repeating times 1.4
b. 3 times 5
c. square root of 2 times square root of 3
d. 4 + 5
e. pi times 3
The correct choices are:
b. 3 times 5
d. 4 + 5
To determine which of the following expressions result in a sum or product that is rational, let's analyze each option:
a. 3.12 repeating times 1.4:
To determine if this product is rational, we need to multiply the two numbers. However, since one of the factors (3.12 repeating) is non-terminating decimal, the product is also a non-terminating decimal and not rational.
b. 3 times 5:
This product is a simple multiplication of two whole numbers, resulting in the rational number 15.
c. square root of 2 times square root of 3:
The product of the square roots of two different numbers is irrational, so this expression does not result in a rational number.
d. 4 + 5:
This sum is a simple addition of two whole numbers, resulting in the rational number 9.
e. pi times 3:
The product of a rational number (3) and an irrational number (pi) is also an irrational number, so this expression does not result in a rational number.
Therefore, the options that result in a sum or product that is rational are:
b. 3 times 5
d. 4 + 5
To determine which of the following options result in a sum or a product that is rational, we need to understand what rational numbers are. Rational numbers are numbers that can be expressed as a fraction, where both the numerator and the denominator are integers.
Let's analyze each option:
a. 3.12 repeating times 1.4:
To check if this product is rational, we need to multiply it and see if the result can be expressed as a fraction. However, 3.12 repeating is a decimal that goes on infinitely, so it cannot be easily expressed as a fraction. Therefore, this product is not rational.
b. 3 times 5:
When we multiply 3 and 5, the result is 15, which is a whole number. Whole numbers can be expressed as a fraction with a denominator of 1. Therefore, this product is rational.
c. square root of 2 times square root of 3:
To determine if this product is rational, we need to evaluate the square roots and multiply them. However, the square root of 2 and the square root of 3 are both irrational numbers. Therefore, this product is not rational.
d. 4 + 5:
When we add 4 and 5, the result is 9, which is a whole number. Therefore, this sum is rational.
e. pi times 3:
Pi (π) is an irrational number that cannot be expressed as a fraction. Therefore, when we multiply it by 3, the result will also be irrational.
In conclusion, the options that result in a sum or a product that is rational are:
b. 3 times 5
d. 4 + 5