Evaluate the sums and determine which statement is true.

To evaluate the sums:

**Column A:**
\(0.7 + 1.8 = 2.5\) (rational)

**Column B:**
\(1 + 0.25 = 1.25\) (rational)

Both sums are rational.

Thus, the correct statement is:
**3. Both Column A and Column B have rational sums.**

The product of a multiplication problem is 144. What do you know about the factors?

If the product of a multiplication problem is 144, then the factors are the numbers that can be multiplied together to get 144.

Here are some key points about the factors of 144:

1. **Pairing Factors:** Factors can be paired. For example, \(1 \times 144\), \(2 \times 72\), \(3 \times 48\), \(4 \times 36\), \(6 \times 24\), \(8 \times 18\), and \(9 \times 16\) are pairs of factors whose product is 144.

2. **Total Factors:** 144 has multiple factors. The complete list of factors includes: \(1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144\).

3. **Prime Factorization:** The prime factorization of 144 is \(2^4 \times 3^2\). This means that the number 144 can be expressed as the product of prime factors raised to their respective powers.

4. **Even and Odd Factors:** All the factors of 144 are even except for 1 and 3.

5. **Perfect Square:** Since \(12 \times 12 = 144\), it is a perfect square.

Overall, factors of 144 are integers that can be multiplied together to give 144, and they can be both even and odd.

Arrange the steps to prove that the

sum t = r + s is irrational if r is rational and s is irrational.

1. Assume for contradiction that t is rational.
2. Write r and s in fractional form.
3. Find a common denominator.
4. Realize a contradiction.

To prove that the sum \( t = r + s \) is irrational if \( r \) is rational and \( s \) is irrational, the steps can be arranged as follows:

1. **Assume for contradiction that t is rational.**
2. **Write r and s in fractional form.**
3. **Find a common denominator.**
4. **Realize a contradiction.**

This arrangement logically follows the process of proof by contradiction. You start by assuming the opposite of what you want to prove (that the sum \( t \) is rational), express the rational and irrational numbers in a suitable form, manipulate them mathematically, and ultimately arrive at a contradiction that reveals the flaw in the initial assumption.

What type of number will the product of π and 5 be?

The product of \( \pi \) (which is an irrational number) and \( 5 \) (which is a rational number) will also be an irrational number.

In general, the product of a nonzero rational number and an irrational number is always irrational. Thus, \( \pi \times 5 \) is irrational.

Complete the expression adding the radicals.

⬜12 +227=14⬜

To complete the expression by adding the radicals, we first simplify each term.

1. Simplify \( \sqrt{12} \):
\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]

2. Simplify \( \sqrt{27} \):
\[
\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}
\]

Now we can add these two simplified radicals together:
\[
2\sqrt{3} + 3\sqrt{3} = (2 + 3)\sqrt{3} = 5\sqrt{3}
\]

Now we can express it as follows:
\[
\boxed{5\sqrt{3} = 14\sqrt{3}}
\]
So the completed expression should read:
\[
\sqrt{12} + \sqrt{27} = 5\sqrt{3}
\]

However, the original expression seems to indicate there's a specific value for the right side of the equation, which may be \( 14\sqrt{3} \) but in a true mathematical sense, the left side should only equal \( 5\sqrt{3} \) unless we're discussing a different context or comparing terms. If you would like clarification or to change the format, please let me know!