Problem 111
Question
Explain how to add \(\sqrt{3}+\sqrt{12}\)
Step-by-Step Solution
Verified Answer
The answer is \(3\sqrt{3}\).
1Step 1: Simplifying the Roots
Simplify the roots. In this case, only \(\sqrt{12}\) can be simplified. Find factors of 12 that are perfect squares because we can take the square root of these factors. The best factor to use in this case would be 4 because it's the highest perfect square that is a factor of 12. We can write \(\sqrt{12}\) as \(\sqrt{4 \times 3}\) which is \(2\sqrt{3}\).
2Step 2: Addition of Similar Terms
Now, the term becomes \(\sqrt{3}+2\sqrt{3}\). Since \(\sqrt{3}\) and \(2\sqrt{3}\) are similar terms, we can add them together to get \(3\sqrt{3}\).
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