Which sum will be irrational?
(1 point)
Responses
3 + 2
3 + 2
start root 19 end root plus start fraction 7 over 2 end fraction
Image with alt text: start root 19 end root plus start fraction 7 over 2 end fraction
Start Fraction 18 over 3 End Fraction plus Start Fraction 11 over ten thousand End Fraction.
Image with alt text: Start Fraction 18 over 3 End Fraction plus Start Fraction 11 over ten thousand End Fraction.
–6 + (–3.251)
–6 + (–3.251)
Which product will be rational?
(1 point)
Responses
17 point Modifying Above 12 with bar times 33
Image with alt text: 17 point Modifying Above 12 with bar times 33
start root 3 end root times start root 9 end root
Image with alt text: start root 3 end root times start root 9 end root
4 times pi
Image with alt text: 4 times pi
negative start root 20 end root times 15
Image with alt text: negative start root 20 end root times 15
Which product will be rational?
(1 point)
Responses
17 point Modifying Above 12 with bar times 33
Image with alt text: 17 point Modifying Above 12 with bar times 33
start root 3 end root times start root 9 end root
Image with alt text: start root 3 end root times start root 9 end root
4 times pi
Image with alt text: 4 times pi
negative start root 20 end root times 15
The sum that will be irrational is the one expressed as √19 + 7/2.
To determine which sum will be irrational, we need to understand what it means for a number to be rational or irrational.
A rational number is a number that can be expressed as a fraction (where the numerator and denominator are integers) or as a terminating or repeating decimal. An irrational number, on the other hand, cannot be expressed as a fraction, and its decimal representation neither terminates nor repeats.
Now, let's consider the given sums:
1) 3 + 2:
This sum is 5, which is a rational number because it can be represented as the fraction 5/1 or the terminating decimal 5. Therefore, the sum of 3 + 2 is rational.
2) start root 19 end root plus start fraction 7 over 2 end fraction:
To determine if this sum is rational or irrational, we need to simplify the expression. The square root of 19 is an irrational number, and adding it to a rational fraction does not change its rationality. Therefore, the sum of start root 19 end root plus start fraction 7 over 2 end fraction is irrational.
3) Start Fraction 18 over 3 End Fraction plus Start Fraction 11 over ten thousand End Fraction:
In this case, the sum can be simplified to 6 + 0.0011, which is a rational number. Since both operands are rational, the sum will also be rational.
4) –6 + (–3.251):
This sum is –9.251, which is a rational number since it can be expressed as the fraction -9251/1000.
Therefore, the sum that will be irrational is the one expressed in option 2: start root 19 end root plus start fraction 7 over 2 end fraction.