91Ó°ÊÓ

A square root is a value that, when multiplied by itself, gives the original number. In math, the square root of a number is often represented by the radical symbol: \( \sqrt{} \). For instance, \( \sqrt{25} = 5 \) because 5 * 5 = 25. The idea is to find what number, when squared (multiplied by itself), results in the original number under the square root.

In our exercise, we need to solve \( \sqrt{12^2} \). To make it easier, we first calculate \( 12^{2} = 144 \). Then, we find the square root of 144, which is 12 because \( 12 * 12 = 144 \).

When simplifying square roots, always check if the number inside the root is a perfect square. If it is, the simplification process becomes straightforward. Otherwise, additional steps might be necessary.

A perfect square is a number that can be expressed as the product of an integer with itself. Examples of perfect squares include 1, 4, 9, 16, 25, and so on.

In our case, 144 is a perfect square because it equals 12 * 12. Recognizing perfect squares is useful for simplifying square roots. Knowing common perfect squares can speed up the process since you can instantly identify their square roots without additional calculation.

Some helpful perfect squares to remember are:

• \( 1^{2} = 1 \)
• \( 2^{2} = 4 \)
• \( 3^{2} = 9 \)
• \( 4^{2} = 16 \)
• \( 5^{2} = 25 \)
• \( 10^{2} = 100 \)
• \( 12^{2} = 144 \)

Mathematical expressions combine numbers, operations (like addition and multiplication), and sometimes variables to describe a value or relationship. In the context of our exercise, \( \sqrt{12^2} \) is an expression that we need to simplify.

Breaking down an expression step-by-step can clarify it. First, identify operations within the expression (like squaring 12). Then, solve each part in sequence. Here, we start by calculating \( 12^{2} \), which equals 144. Next, we take \( \sqrt{144} \) to simplify to 12.

Understanding how to handle different parts of mathematical expressions will help you solve a variety of problems. Always start by performing operations within parentheses or radicals before moving on to other operations like addition or multiplication.