Question

Put the steps in order used to simplify the expression below.
√28 + 3√63
Steps are shown below
1. 11√7
2. 2√7 + 9√7
3. √2•2•7 + 3√3•3•7
4. 2√7 + 3•3√7
5. √4•7 + 3√9•7

Answer 1

To simplify the expression \( \sqrt{28} + 3\sqrt{63} \), we'll follow the steps provided and put them in the correct order:

1. Start with \( \sqrt{28} + 3\sqrt{63} \).

2. Rewrite each square root in terms of their prime factors:
- \( \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \)
- \( \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \)

3. Now the expression is:
\[
2\sqrt{7} + 3\cdot3\sqrt{7} = 2\sqrt{7} + 9\sqrt{7}
\]

4. Combine like terms:
\[
2\sqrt{7} + 9\sqrt{7} = 11\sqrt{7}
\]

Now we can arrange the given steps in the correct order based on how we simplified the expression:

1. **Step 3**: \( \sqrt{2} \cdot 2 \cdot 7 + 3\sqrt{3} \cdot 3 \cdot 7 \)
2. **Step 5**: \( \sqrt{4} \cdot 7 + 3\sqrt{9} \cdot 7 \)
3. **Step 4**: \( 2\sqrt{7} + 3 \cdot 3\sqrt{7} \)
4. **Step 2**: \( 2\sqrt{7} + 9\sqrt{7} \)
5. **Step 1**: \( 11\sqrt{7} \)

So, the correct order of the steps is:
3, 5, 4, 2, 1.