Question

Apply the Closure Property to predict the answer. Will the sum of 25−−√
and 1/8
be an irrational or rational number?(1 point)
Responses

Rational, because both addends are rational.
Rational, because both addends are rational.

It could be either, because there is one of each type of number.
It could be either, because there is one of each type of number.

The sum does not exist because a radical cannot be added to a fraction.
The sum does not exist because a radical cannot be added to a fraction.

Irrational, because one of the addends has a radical.

Answer 1

When proving that the sum of two rational numbers is rational in the expression a+c/bd
, which value could be used for a in order to apply the proof?(1 point)
Responses

π
pi

3–√
Start Root 3 End Root

3
3

30
Start Fraction 3 over 0 End Fraction

Answer 2

stop explaining,
The product of 100−−−√
and 4/15
will be what type of number?(1 point)
Responses

an integer
an integer

zero
zero

irrational
irrational

rational

Answer 3

don't provide any explanation

A rational number and an irrational number are multiplied together. The product is a rational number. What type of rational number must the product be?(1 point)
Responses

zero
zero

an integer
an integer

greater than 1
greater than 1

a perfect square

Answer 4

In order to prove that the sum of two rational numbers, a and b, is rational, put the following steps in the correct order.

Step 1. Identify the sum as rational.

Step 2. Find a common denominator.

Step 3. Write a and b as fractions.

Step 4. Add the fractions.

(1 point)
Responses

Step 3, Step 2, Step 4, Step 1
Step 3, Step 2, Step 4, Step 1

Step 1, Step 3, Step 2, Step 4
Step 1, Step 3, Step 2, Step 4

Step 2, Step 3, Step 4, Step 1
Step 2, Step 3, Step 4, Step 1

Step 1, Step 3, Step 4, Step 2

Answer 5

What type of number will result from 3.4059...−8/5
?(1 point)
Responses

Rational, because one number is rational.
Rational, because one number is rational.

Rational, because both numbers are rational.
Rational, because both numbers are rational.

Irrational, because both numbers are irrational.
Irrational, because both numbers are irrational.

Irrational, because one number is irrational.

Answer 6

To determine whether the sum of \( \sqrt{25} \) and \( \frac{1}{8} \) is rational or irrational, we first evaluate \( \sqrt{25} \).

\[
\sqrt{25} = 5
\]

Now, we can add this rational number to \( \frac{1}{8} \):

\[
5 + \frac{1}{8}
\]

To add these, we can convert \( 5 \) to a fraction with a common denominator:

\[
5 = \frac{40}{8}
\]

Now we can add:

\[
\frac{40}{8} + \frac{1}{8} = \frac{40 + 1}{8} = \frac{41}{8}
\]

Since both \( 5 \) and \( \frac{1}{8} \) are rational numbers, their sum \( \frac{41}{8} \) is also a rational number.

Thus, the answer is:

**Rational, because both addends are rational.**

Answer 7

In order to determine a suitable value for \( a \) when proving that the sum of two rational numbers is rational, we need to ensure that \( a \) is a rational number itself.

The rational numbers are those that can be expressed as the quotient of two integers (where the denominator is not zero). Let's analyze the given options:

1. **π (pi)**: This is an irrational number.
2. **\(\sqrt{3}\)**: This is also an irrational number.
3. **3**: This is a rational number since it can be written as \(\frac{3}{1}\).
4. **\(\frac{3}{0}\)**: This is undefined since division by zero is not allowed.

Hence, the only suitable choice for \( a \) that allows us to apply the proof for the sum of two rational numbers being rational is:

**3**.

Answer 8

The product of \( \sqrt{100} \) and \( \frac{4}{15} \) will be:

\[
\sqrt{100} = 10
\]

Now multiply by \( \frac{4}{15} \):

\[
10 \times \frac{4}{15} = \frac{40}{15} = \frac{8}{3}
\]

Since \( \frac{8}{3} \) is a fraction (the ratio of two integers), this product is a rational number.

So the answer is:

**rational**.

Answer 9

**zero**.

Answer 10

**Step 3, Step 2, Step 4, Step 1**

Answer 11

**Rational, because both numbers are rational.**