UpStudy Free Solution:

When adding expressions involving square roots, you can only combine like terms. In this case, \(2\sqrt { 3} \) and \(3\sqrt { 2} \) are not like terms because the square roots are different.
Therefore, the sum of \(2\sqrt { 3} \) and \(3\sqrt { 2} \) is simply:
\[2\sqrt { 3} + 3\sqrt { 2} \]
This expression cannot be simplified further.

Supplemental Knowledge

When dealing with algebraic expressions involving square roots, it is important to understand the properties of radicals. Radicals can often be simplified or combined if they are like terms (i.e., they have the same radicand). However, if the radicands are different, as in this case (\(\sqrt { 3} \) and \(\sqrt { 2} \)), they cannot be directly added together.
Key Concepts:

Like Radicals:

Like radicals have the same radicand and can be combined by adding or subtracting their coefficients.

Example: \(a\sqrt { b} + c\sqrt { b} = ( a + c) \sqrt { b} \)

Unlike Radicals:

Unlike radicals have different radicands and cannot be combined directly.

Example: \(a\sqrt { b} + c\sqrt { d} \) remains as it is unless \(b = d\).

Simplifying Radicals:

Sometimes, radicals can be simplified if the radicand has a perfect square factor.

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