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. Adding a radical to a rational number does not always result in an irrational number. For example, if you add the square root of 4 (which is a rational number, equal to 2) to the rational number 3, the sum is 5, which is a 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?(1 point)

Responses

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.

Yes, radicals are irrational.
Yes, radicals are irrational.

No, radicals always simplify to integers, so they are rational.

No, some radicals simplify to rational numbers.

How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point)

Responses

Irrational numbers can be added or subtracted.
Irrational numbers can be added or subtracted.

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 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 of an irrational and rational number can’t be predicted.

The sum or difference of a rational and irrational number is a rational number.

What type of number will result from the expression 19−−√−32?(1 point)

Responses

an irrational number
an irrational number

a rational number
a rational number

an integer
an integer

a whole number

The type of number that will result from the expression 19−−√−32 is an irrational number.

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?(1 point)

Responses

by using a proof by contradiction to show multiplication is a closed operation for rational numbers
by using a proof by contradiction to show multiplication is a closed operation for rational numbers

by choosing random numbers to plug into multiplication problems until he’s convinced
by choosing random numbers to plug into multiplication problems until he’s convinced

He’s correct; it is impossible to prove in any way.
He’s correct; it is impossible to prove in any way.

by creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer

By creating a proof that shows directly how multiplying a rational and irrational number leads to an irrational answer.

Question

Find the product of 12−−√ and 56. What type of number is it?(1 point)
Responses

4.2974 . . . ; an irrational number
4.2974 . . . ; an irrational number

4.1569 . . . ; an irrational number
4.1569 . . . ; an irrational number

2.8867 . . . ; an irrational number
2.8867 . . . ; an irrational number

2.6307 . . . ; an irrational number

The product of 12−−√ and 56 is 2.8867... which is an irrational number.