Question

Put the steps in order used to simplify the expression below. 28−−√+363−−√28+363 (5 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.  27–√+97–√27+97  2⋅2⋅7−−−−−−√+33⋅3⋅7−−−−−−√2⋅2⋅7+33⋅3⋅7  117–√117  4⋅7−−−−√+39⋅7−−−−√4⋅7+39⋅7  27–√+3⋅37–√27+3⋅37

Answer 1

To simplify the expression \( \sqrt{28} + \sqrt{36} \), we can follow these steps in order:

1. **Rewrite each square root in terms of its prime factors**:
- \( \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \)
- \( \sqrt{36} = \sqrt{6^2} = 6 \)

So, the expression becomes:
\( 2\sqrt{7} + 6 \).

2. **Combine the results**:
\( 2\sqrt{7} + 6 \).

Now, let’s match these steps with the provided responses:

1. \( \sqrt{28} + \sqrt{36} \) --> This matches the initial expression.
2. \( 2 \cdot 2 \cdot \sqrt{7} + 3 \cdot 3 \cdot \sqrt{4} \) --> This simplifies to \( 2\sqrt{7} + 6 \).
3. \( 2\sqrt{7} + 3 \cdot 6 \).
4. \( 2\sqrt{7} + 6 \).

3. **Final expression**: The expression has been simplified stepwise to its final form \( \sqrt{117} \).

Let's arrange the steps in the correct order:

1. \( \sqrt{28} + \sqrt{36} \)
2. \( 2 \cdot 2 \cdot 7 + 3 \cdot 3 \cdot 6 \)
3. \( 2\sqrt{7} + 6 \)
4. \( \sqrt{117} \)

Therefore, the order of operations is:

1. \( \sqrt{28} + \sqrt{36} \)
2. \( 2 \cdot 2 \cdot 7 + 3 \cdot 3 \cdot 6 \)
3. \( 2\sqrt{7} + 6 \)
4. \( \sqrt{117} \)

The final correct order of simplification responses in relation to the problem's context should be structured as per above-listed points.