To simplify the expression \(\sqrt{28} + 3\sqrt{63}\), we can follow these steps in the correct order:
-
Factor the square roots:
- \(\sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7}\)
- \(\sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7}\)
-
Substitute these values back into the expression:
- So, we have \(\sqrt{28} + 3\sqrt{63} = 2\sqrt{7} + 3(3\sqrt{7})\)
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Multiply the coefficients:
- \(3(3\sqrt{7}) = 9\sqrt{7}\)
-
Combine like terms:
- \(2\sqrt{7} + 9\sqrt{7} = (2 + 9)\sqrt{7} = 11\sqrt{7}\)
Thus, the correct order of the steps used to simplify the expression \(\sqrt{28} + 3\sqrt{63}\) is:
- \(\sqrt{28} = \sqrt{4 \cdot 7} + 3\sqrt{63} = 3\sqrt{9 \cdot 7}\)
- \(\sqrt{4} \cdot \sqrt{7} + 3\sqrt{9} \cdot \sqrt{7}\)
- \(2\sqrt{7} + 3 \cdot 3\sqrt{7}\)
- \(2\sqrt{7} + 9\sqrt{7}\)
- \(11\sqrt{7}\)
Hence, the final correct answer is \(11\sqrt{7}\).
In conclusion, the steps in order for simplifying the expression are:
- \(\sqrt{4 \cdot 7} + 3\sqrt{9 \cdot 7}\)
- \(2\sqrt{7} + 3 \cdot 3\sqrt{7}\)
- \(2\sqrt{7} + 9\sqrt{7}\)
- \(11\sqrt{7}\)
The correct order of the answer choices would then be:
- \(\sqrt{4 \cdot 7} + 3\sqrt{9 \cdot 7}\)
- \(\sqrt{2 \cdot 2 \cdot 7} + 3\sqrt{3 \cdot 3 \cdot 7}\)
- \(2\sqrt{7} + 9\sqrt{7}\)
- \(11\sqrt{7}\)
And the last step gives you the final answer: \(11\sqrt{7}\).