Question

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)

Answer 1

What type of number will result from the sum of 2/3
and 25−−√
?

rational
irrational
whole number
zero
Enter the number that corresponds to the correct answer.

(1 point)
The sum of 2/3
and 25−−√
will result in the type of number described by Option #
.

Answer 2

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.

Answer 3

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 #

Answer 4

The sum of a rational number and an irrational number will result in an **irrational** number.

So the correct answer is:

**irrational**

Answer 5

The sum of \( \frac{2}{3} \) (a rational number) and \( \sqrt{25} \) (which is equal to 5, a rational number) will result in a rational number.

So the correct answer is:

**rational**

Answer 6

Let's break down the expression \( \sqrt{8} + \frac{3}{2} \).

1. \( \sqrt{8} \) is an **irrational** number.
2. \( \frac{3}{2} \) is a **rational** number.

According to the rules of arithmetic with rational and irrational numbers:
- The sum of a rational number and an irrational number is always **irrational**.

Given this information:

- **Machir's claim** is incorrect because \( \sqrt{8} \) is not rational.
- **Sofia's claim** is incorrect because \( \sqrt{8} \) is not rational.
- **Lexi's claim** is correct because the sum of an irrational number (\( \sqrt{8} \)) and a rational number (\( \frac{3}{2} \)) is irrational.

Therefore, the correct answer is:

**Person 3 is correct.**

Answer 7

Let's analyze the product of \( \sqrt{36} \) and \( \frac{1}{2} \):

1. \( \sqrt{36} = 6 \), which is a **rational** number.
2. \( \frac{1}{2} \) is also a **rational** number.

When you multiply two rational numbers, the result is always a rational number.

The product of \( \sqrt{36} \) and \( \frac{1}{2} \) will therefore be:

\[
6 \times \frac{1}{2} = 3
\]

Since 3 is a rational number, the answer is:

**rational**