The product of a multiplication problem is √225

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.

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

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.

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

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.

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

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.

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.

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.

rewrite 25^1/4 as a root

25^(1/4) can be written as the fourth root of 25, symbolized as √[4]{25}.

rewrite 27^3/4 as a root number

27^(3/4) can be written as the fourth root of 27 cubed, represented as ∛[4]{27^3}.

Write an equivalent expression for -(b^1/4)^12

An equivalent expression for -(b^(1/4))^12 would be -b^(3/2).

is 47/3 + 11 rational

Yes, 47/3 + 11 is a rational number. The sum of two rational numbers is always rational.

Is 2π x 3/4 rational?

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.