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A square root is a value that, when multiplied by itself, produces the original number. In mathematical terms, if you have a number like 9, the square root of 9 (written as \( \sqrt{9} \)) is 3, since \( 3 \times 3 = 9 \). Understanding square roots is key in simplifying expressions involving them.

If we take the example of simplifying the expression \( \sqrt{9} \)+\( \sqrt{16} \), we start by identifying the square roots. The square root of 9 is 3 and the square root of 16 is 4. We then proceed to add these results, which gives us a simplified expression of 7.

Basic arithmetic includes the primary operations of addition, subtraction, multiplication, and division. These operations are fundamental to all areas of mathematics and are used in simplifying expressions, solving equations, and manipulating numbers.

In the given exercise, addition is the key arithmetic operation used. After identifying the square roots as 3 and 4, the next step is simply adding these numbers together. The expression \( \sqrt{9} \) + \( \sqrt{16} \) therefore simplifies to 3 + 4, which equals 7.

Understanding how to perform these basic operations quickly and accurately is essential for progressing to more complex mathematical concepts.

Mathematical operations are procedures or functions that take one or more numbers as input and produce a number as output. The main operations include addition, subtraction, multiplication, and division, but they also extend to include operations such as squaring and finding square roots.

In our example, we're dealing primarily with the operations of finding square roots and addition. Calculating the square roots \( \sqrt{9} \) and \( \sqrt{16} \) involves determining what number squared gives the original number. Once these square roots are found (3 and 4, respectively), the operation of addition combines them into a final result of 7.

Mastering these basic mathematical operations allows for more complex problem solving and helps in understanding higher-level math concepts more effectively.