According to the Closure Property, which of these sums results in a rational number?
a. π+√4
b. 0.643892553…+ 3/4
c. 0.6¯¯¯¯ + 9/10
d. √36 + √221
The Closure Property states that if you add two rational numbers, the result will always be a rational number.
Out of the given options:
a. π+√4 = irrational + rational = irrational
b. 0.643892553…+ 3/4 = rational + rational = rational
c. 0.6¯¯¯¯ + 9/10 = rational + rational = rational
d. √36 + √221 = rational + irrational = irrational
Therefore, the sum that results in a rational number is option b. 0.643892553…+ 3/4.
is the product of 4/5 and 15 rational or irrational
The product of 4/5 and 15 is rational.
To determine this, we can simplify the expression 4/5 * 15. The product is (4 * 15) / 5 = 60/5 = 12.
Since 12 can be expressed as a ratio of two integers (12/1), it is a rational number.
How does the Closure Property prove that the sum of a rational and irrational number is irrational?
a. Irrational numbers can be added or subtracted.
b. The sum or difference of two rational numbers is a rational number.
c. The sum of an irrational and rational number can’t be predicted.
d. The sum or difference of a rational and irrational number is a rational number.
The Closure Property does not prove that the sum of a rational and irrational number is irrational.
The answer to your question would be c. The sum of an irrational and rational number can't be predicted. The sum or difference of a rational and irrational number does not follow a specific pattern and can result in either an irrational or rational number.
Mia says that anytime there is a radical in an addition expression, it automatically has an irrational number as the sum. Is she correct?
No, Mia is not correct. The sum of an expression that includes a radical (square root) is not automatically an irrational number.
There are cases where the sum of an expression with a radical can result in an irrational number, but it is not true for all cases. It depends on the specific numbers involved in the expression.
For example, the sum of √4 + √4 equals 2 + 2 = 4, which is a rational number.
Therefore, Mia's statement is incorrect. The sum of an expression with a radical can be either rational or irrational, depending on the specific numbers involved.
Mia says that anytime there is a radical in an addition expression, it automatically has an irrational number as the sum. Is she correct?(1 point) Responses Yes, radicals are irrational. Yes, radicals are irrational. No, radicals always simplify to integers, so they are rational. No, radicals always simplify to integers, so they are rational. Yes, radicals can’t be simplified, so they must be irrational. Yes, radicals can’t be simplified, so they must be irrational. No, some radicals simplify to rational numbers. No, some radicals simplify to rational numbers.
The correct response is "No, some radicals simplify to rational numbers."
What type of number will result from the expression √19 - 3/2
a rational number
a whole number
an integer
an irrational number
The expression √19 - 3/2 will result in an irrational number.
The square root of 19 is an irrational number, and when you subtract a rational number (3/2) from it, the result will still be irrational.
Ryiaz claims it is impossible to prove that a rational number multiplied by an irrational number gives an irrational product. How can you prove this?
by creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer
by using a proof by contradiction to show multiplication is a closed operation for rational numbers He’s correct; it is impossible to prove in any way.
by choosing random numbers to plug into multiplication problems until he’s convinced
The correct response is "by creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer."
It is indeed possible to prove that multiplying a rational number by an irrational number leads to an irrational product. This can be done by providing a proof that demonstrates the properties of rational and irrational numbers in relation to multiplication and how their combination results in an irrational number.