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
No, some radicals simplify to rational numbers.
No, some radicals simplify to rational numbers.
Yes, radicals are irrational.
Yes, radicals are irrational.
Yes, radicals can’t be simplified, so they must be irrational.
Yes, radicals can’t be simplified, so they must be irrational.
No, radicals always simplify to integers, so they are rational.
No, some radicals simplify to rational numbers.
What type of number will result from the expression √19 − 3/2?(1 point)
Responses
a rational number
a rational number
an integer
an integer
a whole number
a whole number
an irrational number
an irrational number
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 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
He’s correct; it is impossible to prove in any way.
He’s correct; it is impossible to prove in any way.
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
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
Find the product of √12 and 5/6 What type of number is it?(1 point)
Responses
2.6307 . . . ; an irrational number
2.6307 . . . ; an irrational number
4.2974 . . . ; an irrational number
4.2974 . . . ; an irrational number
2.8867 . . . ; an irrational number
2.8867 . . . ; an irrational number
4.1569 . . . ; an irrational number
4.2974...; an irrational number
thanks
You're welcome! If you have any more questions, feel free to ask.
The correct response is: No, some radicals simplify to rational numbers.
To verify Mia's statement, we need to understand what a radical is and how it relates to irrational numbers. A radical is a symbol denoted √, where you take the square root of a number. For example, √9 equals 3, since 3 multiplied by itself equals 9.
Now, let's examine Mia's statement. She claims that any addition expression with a radical always has an irrational number as the sum. However, this is not correct. Consider the expression √4 + √4. Each radical simplifies to 2, and the sum is 2 + 2 = 4, which is a rational number.
This example demonstrates that not all addition expressions with radicals result in irrational numbers. Therefore, Mia's statement is incorrect. Some radicals can indeed simplify to rational numbers.