What type of number will result from the sum of a rational number and irrational number?

Question

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

(1 point)

Answer 1

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

So the correct answer is:

irrational

Answer 2

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 3

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 4

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 5

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 6

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 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