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: $$2\sqrt{7}+3\cdot 3\sqrt{7}=2\sqrt{7}+9\sqrt{7}$$

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.