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Chapter 0: Problem 111

Explain how to add \(\sqrt{3}+\sqrt{12}\)

Short Answer

Expert verified
The answer is \(3\sqrt{3}\).

Step by step solution

01

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 \(2\sqrt{3}\).
02

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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