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.
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.