Perform the indicated operation, leaving all answers in simplest form.(5 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Simplify the following:
108
−
−
−
√
108=
Response area

15
−
−
√
⋅
5
–
√
15⋅5=
Response area

12
2
3
√
1223=
Response area

4
3
–
√
+
27
−
−
√
43+27=
Response area

3
12
−
−
√
−2
3
–
√
312−23=
Response area

5
3
–
√
53
2
3
–
√
23
3
12
−
−
√
312
4
3
–
√
43
7
3
–
√
73
3
–
√
3
75
−
−
√
75
3
3
–
√
33
4
3
–
√
+
27
−
−
√
43+27
6
3
–
√
63
3
12
−
−
√
−2
3
–
√
312−23
6
3
√
3
633
8
3
–
√
83

Answer 1

Let's simplify each expression in the format provided.

1. Simplify \( \sqrt{108} \):

   \[ \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \cdot \sqrt{3} = 6\sqrt{3} \] Response area: \( 6\sqrt{3} \)

2. Simplify \( \sqrt{15} \cdot 5 \):

   \[ \sqrt{15} \cdot 5 = 5\sqrt{15} \] Response area: \( 5\sqrt{15} \)

3. Simplify \( \sqrt{1223} \) (this needs to be factored):

   The number 1223 doesn't have a perfect square factor, so \( \sqrt{1223} \) cannot be simplified further. If you intend to express it in simplest form: Response area: \( \sqrt{1223} \)

4. Simplify \( \sqrt{43 + 27} \):

   \[ \sqrt{43 + 27} = \sqrt{70} \] Response area: \( \sqrt{70} \)

5. Simplify \( \sqrt{312 - 23} \):

   \[ 312 - 23 = 289 \Rightarrow \sqrt{289} = 17 \] Response area: \( 17 \)

6. Simplify \( \sqrt{53} + 2 \):

   This cannot be simplified further as \( \sqrt{53} \) does not have a perfect square factor. Response area: \( \sqrt{53} + 2 \)

7. Similarly, the other terms can be simplified similarly.

If you have specific details on what is requested for other expressions, please clarify, and I will be happy to assist!