Put the steps to the proof that the sum t=r+s

Question

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.

(1 point)
Responses

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

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

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

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

Answer 1

To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, the correct sequence of steps is:

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.

Thus, the correct response is:

Step 2, Step 4, Step 1, Step 3

Answer 2

What type of number will the product of π
and 34
be?(1 point)
Responses

a rational number
a rational number

an irrational number
an irrational number

a radical
a radical

a repeating decimal

Answer 3

The product of \( \pi \) (an irrational number) and 34 (a rational number) will be an irrational number.

Therefore, the correct response is:

an irrational number.