The product of 100−−−√

Question

and 4/15
will be what type of number?(1 point)
Responses

rational
rational

irrational
irrational

an integer
an integer

zero

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

greater than 1
greater than 1

an integer
an integer

a perfect square

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

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

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

Step 3, Step 2, Step 4, Step 1

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

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

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

Irrational, because one number is irrational.
Irrational, because one number is irrational.

Irrational, because both numbers are irrational.

What type of number will result from multiplying −8–√
and 4/5
?(1 point)
Responses

the number zero
the number zero

a rational number
a rational number

an irrational number
an irrational number

an integer

Simon, Asia, and Jiovanni are finding the product of a rational and irrational number.

Simon says the result should be irrational because the product of an irrational and rational number is always irrational.

Asia says the result should be zero because the product of an irrational and rational number is always zero.

Jiovanni says the result should be rational because the product of an irrational and rational number is always rational.

Who is correct?

(1 point)
Responses

Jiovanni
Jiovanni

Simon
Simon

None of them are correct.
None of them are correct.

Asia

What is the correct simplification of 64^4/3
?(1 point)
Responses

4,096
4,096

85.3
85.3

16
16

256

What is the correct simplification of 125^4/3
?(1 point)
Responses

125
125

625
625

5
5

25

Answer 1

Let's go through each question one by one.

1. The product of \( \sqrt{100} \) and \( \frac{4}{15} \) will be what type of number?

   • The square root of 100 is 10, which is a rational number. Multiplying a rational number (\(10\)) by another rational number (\( \frac{4}{15} \)) results in a rational number.
   • Response: rational

2. 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?

   • The product of a rational number and an irrational number is typically irrational. Thus, the scenario given seems flawed. However, if we were to consider only rational numbers multiplying and ensuring it stayed rational, it must hold value within rational constraints.
   • Response: (None of the provided responses directly fit, as the product of a rational and irrational number is irrational. Assuming rational numbers only, this is tricky. Let's select based on a bound). This may interpret as rational options.

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

   • Correct Order: Step 3 (Write a and b as fractions), Step 2 (Find a common denominator), Step 4 (Add the fractions), Step 1 (Identify the sum as rational).
   • Response: Step 3, Step 2, Step 4, Step 1

4. What type of number will result from \( 3.4059... - \frac{8}{5} \)?

   • \( 3.4059... \) is a rational number since it has a repeating decimal representation (assuming other conditions). \( \frac{8}{5} \) is clearly rational. The subtraction of two rational numbers is rational.
   • Response: Rational, because both numbers are rational.

5. What type of number will result from multiplying \( -\sqrt{8} \) and \( \frac{4}{5} \)?

   • \( -\sqrt{8} \) is an irrational number and \( \frac{4}{5} \) is rational. The product of a rational number (non-zero) and an irrational number is irrational.
   • Response: an irrational number

6. Simon, Asia, and Jiovanni are finding the product of a rational and irrational number.

   • Simon is correct; the product of a rational and an irrational number is always irrational (unless that rational number is zero, but in your question, it isn't specified that any of them is).
   • Response: Simon

7. What is the correct simplification of \( 64^{4/3} \)?

   • This can be calculated as \( (64^{1/3})^4 = 4^4 = 256 \).
   • Response: 256

8. What is the correct simplification of \( 125^{4/3} \)?

   • This can be calculated as \( (125^{1/3})^4 = 5^4 = 625 \).
   • Response: 625

If this aligns with your intents, you're all set! Let me know if something else is required!