Which product will be rational?
A. 17 point Modifying Above 12 with bar times 33
B. start root 3 end root times start root 9 end root
C. 4 times pi
D. negative start root 20 end root times 15
C. 4 times pi.
To determine which product is rational, we need to identify which expression results in a rational number. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers.
Let's analyze each of the given options:
A. 17 point Modifying Above 12 with bar times 33
The given expression seems unclear, so it is difficult to determine if it is rational.
B. start root 3 end root times start root 9 end root
Simplifying this expression, we have √3 * √9 = √3 * 3 = 3√3. This is an irrational number since it contains the square root of a non-perfect square (√3).
C. 4 times pi
Multiplying 4 by pi (approximately 3.14159) results in a product that is an irrational number. Therefore, this option is not rational.
D. negative start root 20 end root times 15
Simplifying this expression, we have -√20 * 15. Since √20 can be simplified to 2√5, we have -2√5 * 15 = -30√5. This is an irrational number since it contains the square root of a non-perfect square (√5).
Therefore, none of the given options (A, B, C, or D) represent a rational number.
To determine which product is rational among the given options, we need to understand what a rational number is.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number can be written in the form a/b, where a and b are integers.
Let's analyze each option:
A. 17 point Modifying Above 12 with bar times 33:
The presence of decimal points and bars suggests that this number might be irrational. To determine if it is rational, we need more information or the exact representation of this number.
B. start root 3 end root times start root 9 end root:
In this option, we have the square root of 3 multiplied by the square root of 9. The square root of 3 is an irrational number, but the square root of 9 is 3, which is a rational number. Since the product of a rational and an irrational number is irrational, this option is irrational.
C. 4 times pi:
Pi (π) is an irrational number, meaning it cannot be expressed as a fraction. However, since 4 is a rational number, the product of 4 and π will still be an irrational number.
D. negative start root 20 end root times 15:
In this option, we have the negative square root of 20 multiplied by 15. The square root of 20 is an irrational number. When multiplied by a rational number, the result remains irrational.
Based on the analysis above, none of the given options represent rational numbers.