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When simplifying radical expressions, it's important to identify like terms. Like terms have the same radical part. In the exercise, the terms are \(3 \sqrt{h}\) and \(7 \sqrt{h}\). Both have the same radical part \(\sqrt{h}\).
Like terms in radical expressions can only be combined if their radical parts (everything under the square root) are identical. For instance, \(\sqrt{h}\) and \(5\sqrt{h}\) are like terms, whereas \(\sqrt{h}\) and \(\sqrt{k}\) are not.

• Example: \sqrt{2}\ and \sqrt{2}\ are like terms.
• Non-Example: \sqrt{2}\ and \sqrt{3}\ are not like terms.

Recognizing like terms helps simplify the expression by combining them.

After identifying like terms, the next step is to combine the coefficients. Coefficients are the numbers in front of the radicals.
In the exercise, the coefficients are 3 and 7 in \(3 \sqrt{h}\) and \(7 \sqrt{h}\), respectively. To combine them, you simply add the coefficients: \(3 + 7 = 10\).
By adding these coefficients, you create a new, single term. This simplifies the problem and makes calculations easier.

• Example: Combining coefficients in \(4 \sqrt{x}\ + 5 \sqrt{x}\) would be \(4 + 5 = 9\).

Combining coefficients only works with like terms. This means the radicals have to be exactly the same.

Radicals, especially square roots, often appear in mathematics. A radical is an expression that incorporates a root symbol \(\sqrt{}\). Radicals can represent numbers, variables, or more complex forms.
For instance, \(\sqrt{h}\) in the exercise is a radical. Simplifying radicals often involves removing or combining these roots.
Understanding radicals makes it easier to handle different types of algebraic operations.
Here are some basic properties of radicals:

• Radicals can be multiplied and divided: \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).
• You can commonly add or subtract radicals with the same radicand (the number or expression under the root): \(a \sqrt{c} + b \sqrt{c} = (a+b) \sqrt{c}\).

Recognizing and manipulating radicals is a key skill in algebra and beyond. Simplifying expressions by combining like terms and coefficients helps achieve cleaner, more manageable equations. In our exercise, we concluded with \(10 \sqrt{h}\). The 10 is the combined coefficient, and the \(\sqrt{h}\) is the radical part.