Problem 122 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The result of \(\sqrt{3}+\sqrt{12}\) is \(3*\sqrt{3}\)

Step 1: Simplify the square roots

First we have to simplify \(\sqrt{12}\). We find the prime factorization of 12, which is 2*2*3. This allows us to rewrite \(\sqrt{12}\) as \(\sqrt{2^2*3}\). Using the rule that \(\sqrt{a*b} = \sqrt{a} * \sqrt{b}\), we can convert this into \(2*\sqrt{3}\). So, our initial expression \(\sqrt{3} + \sqrt{12}\) changes to \(\sqrt{3} + 2*\sqrt{3}\).

Step 2: Combine like terms

We treat the square roots like variables. This means we can add their coefficients (the numbers in front of them) just like simple numbers. So, \(\sqrt{3} + 2*\sqrt{3}\) simplifies to \(3*\sqrt{3}\).