Put the steps in order used to simplify the expression below.

Question

√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.