What type of number will result from the sum of a rational number and irrational number?
irrational
rational
zero
equal
Enter the number that corresponds to the correct answer.
(1 point)
Option #
describes the sum of a rational number and irrational number.
The correct answer is Option #1: irrational. The sum of a rational number and an irrational number will always be an irrational number. This is because the irrational component cannot be eliminated or canceled out by the rational component, resulting in an irrational value.
What type of number will result from the sum of 23
and 25−−√
?
rational
irrational
whole number
zero
Enter the number that corresponds to the correct answer.
(1 point)
The sum of 23
and 25−−√
will result in the type of number described by Option #
.
Machir, Sofia, and Lexi are discussing the result of the sum of √8 + 3/2
.
Machir says the answer is irrational because both numbers are irrational.
Sofia says the answer is rational because both numbers are rational.
Lexi says the result is irrational because one number is irrational and the other is rational.
Who is correct?
1. Machir
2. Sofia
3. Lexi
(1 point)
Person #
is correct.
The correct answer is Person #3: Lexi.
The sum of √8 and 3/2 will result in an irrational number. This is because √8 is an irrational number and 3/2 is a rational number. When adding these two together, the result cannot be simplified to a rational number, therefore it is an irrational number. Lexi's statement correctly identifies this fact.
What type of number will result from the product of √36
and 1/2
? Enter the number that corresponds to the correct answer.
rational
irrational
mixed number
zero
(1 point)
The product of √36
and 1/2
will result in the type of number described by Option #
.
The correct answer is Option #1: rational. The product of √36 and 1/2 will result in a rational number. √36 is equal to 6, which is a rational number. When multiplied by 1/2, the result will still be a rational number. Therefore, the product will be a rational number.
Elaina, Miguel, and Swati are calculating the product of √6
and 2/3
.
Elaina says the answer is irrational because both numbers are irrational.
Miguel says the answer is rational because both numbers are rational.
Swati says the answer is irrational because one number is rational and the other number is irrational.
Who is correct? Enter the number that corresponds to the correct answer.
Elaina
Miguel
Swati
(1 point)
Person #
is correct.
The correct answer is Person #3: Swati.
The product of √6 and 2/3 will result in an irrational number. This is because √6 is an irrational number and 2/3 is a rational number. When multiplying these two together, the result cannot be simplified to a rational number, therefore it is an irrational number. Swati's statement correctly identifies this fact.
How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point)
Responses
The sum or difference of a rational and irrational number is a rational number.
The sum or difference of a rational and irrational number is a rational number.
The sum or difference of two rational numbers is a rational number.
The sum or difference of two rational numbers is a rational number.
The sum of an irrational and rational number can’t be predicted.
The sum of an irrational and rational number can’t be predicted.
Irrational numbers can be added or subtracted.
The correct answer is "The sum or difference of a rational and irrational number is a rational number."
The Closure Property of addition states that if you add two numbers, the result is always a number of the same type. In this case, if you add a rational number and an irrational number, the result will be a rational number. Therefore, "The sum or difference of a rational and irrational number is a rational number." is the answer that explains how the Closure Property proves that the sum of a rational and irrational number is rational.