Question

The product of a multiplication problem is √225
What do you know about the factors?

A. They are both rational because the product is rational.

B. At least one factor is irrational because the product is irrational.

C. It cannot be predicted based on the information given.

D. One factor is rational, but the other is irrational.
Answer
Put the steps to the proof that the sum t=r+s is irrational if r is a rational and s is rational in the correct sequence.

Step 1. Subtract, writing s as a fraction.

Step 2. For a contradiction, assume that t is rational, and write r and t as fractions.

Step 3. Realize a contradiction.

Step 4. Find a common denominator.

A. Step 4, Step 2, Step 1, Step 3

B. Step 2, Step 4, Step 1, Step 3

C. Step 1, Step 3, Step 2, Step 4

D. Step 3, Step 4, Step 2, Step 1
Answer
What type of number will the product of π and 34 be?

A. a radical

B. an irrational number

D. a rational number

C. a repeating decimal
Answer
What type of number will the product of π and 3/4 be?

A. a radical

B. an irrational number

D. a rational number

C. a repeating decimal
Answer
Prove that the product of the two rational numbers √36 and 5/3 is a rational number. Find the product and explain how you know it is a rational number. Explain your reasoning in 1–2 sentences.
Answer
rewrite 25^1/4 as a root
Answer
rewrite 27^3/4 as a root number
Answer
Write an equivalent expression for -(b^1/4)^12
Answer
is 47/3 + 11 rational
Answer
Is 2π x 3/4 rational?
Answered by GPT 3.5
The correct answer is D. One factor is rational, but the other is irrational.

The square root of 225 (√225) can be written as 15. 15 is a rational number since it can be expressed as a fraction (15/1). Therefore, one factor is rational.

The other factor can be found by dividing 225 by 15, which equals 15. 15 is not a rational number because it cannot be expressed as a fraction, so it is an irrational number. Therefore, the other factor is irrational.
Answered by GPT 3.5
The correct sequence is:

B. Step 2, Step 4, Step 1, Step 3.

Step 2. For a contradiction, assume that t is rational, and write r and t as fractions.
Step 4. Find a common denominator.
Step 1. Subtract, writing s as a fraction.
Step 3. Realize a contradiction.
Answered by GPT 3.5
The correct answer is B. an irrational number.

The number π (pi) is an irrational number, meaning it cannot be expressed as a fraction or a terminating or repeating decimal. Multiplying an irrational number by a rational number does not change the irrationality of the number. Therefore, the product of π and 34 would also be an irrational number.
Answered by GPT 3.5
The correct answer is B. an irrational number.

The number π (pi) is an irrational number, and multiplying it by any rational number will result in an irrational number. The product of π and 3/4 would also be an irrational number.
Answered by GPT 3.5
To prove that the product of √36 and 5/3 is a rational number, we first calculate the product. √36 is equal to 6, therefore the product of 6 and 5/3 is 10/3, which is a fraction. Since the product is a fraction, it is considered a rational number.
Answered by GPT 3.5
25^(1/4) can be written as the fourth root of 25, symbolized as √[4]{25}.
Answered by GPT 3.5
27^(3/4) can be written as the fourth root of 27 cubed, represented as ∛[4]{27^3}.
Answered by GPT 3.5
An equivalent expression for -(b^(1/4))^12 would be -b^(3/2).
Answered by GPT 3.5
Yes, 47/3 + 11 is a rational number. The sum of two rational numbers is always rational.
Answered by GPT 3.5
No, 2π x 3/4 is not a rational number. The value of 2π is irrational, and multiplying an irrational number by a rational number does not change its irrationality. Therefore, the product will still be irrational.