Put the steps in order used to simplify the expression below sqrt(28) + 3sqrt(63) (5 points) equiv sqrt 4*7 +3 sqrt 9*7; equiv sqrt 2*2*7 +3 sqrt 3*3*7; equiv2 sqrt 7 +9 sqrt 7; equiv2 sqrt 7 +3*3 sqrt 7; equiv11 sqrt 7

Answer 1

To simplify the expression \(\sqrt{28} + 3\sqrt{63}\), follow these steps in the correct order:

1. Start with the original expression:
   \(\sqrt{28} + 3\sqrt{63}\)

2. Factor the square roots: \(\equiv \sqrt{4 \cdot 7} + 3 \sqrt{9 \cdot 7}\)

3. Simplify the square roots: \(\equiv \sqrt{2^2 \cdot 7} + 3 \sqrt{3^2 \cdot 7}\)

4. Use the property \(\sqrt{a^2} = a\): \(\equiv 2\sqrt{7} + 3 \cdot 3\sqrt{7}\)

5. Calculate the coefficients: \(\equiv 2\sqrt{7} + 9\sqrt{7}\)

6. Combine the like terms: \(\equiv (2 + 9)\sqrt{7}\)

7. Final answer: \(\equiv 11\sqrt{7}\)

So, the correct order is:

1. \(\sqrt{28} + 3\sqrt{63}\)
2. \(\equiv \sqrt{4 \cdot 7} + 3 \sqrt{9 \cdot 7}\)
3. \(\equiv \sqrt{2^2 \cdot 7} + 3 \sqrt{3^2 \cdot 7}\)
4. \(\equiv 2\sqrt{7} + 3 \cdot 3\sqrt{7}\)
5. \(\equiv 2\sqrt{7} + 9\sqrt{7}\)
6. \(\equiv 11\sqrt{7}\)

Therefore, the final simplified expression is \(11\sqrt{7}\).