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Chapter 2: Problem 74

Simplify. $$12^{2}$$

Short Answer

Expert verified
The simplified form of \(12^2\) is 144.

Step by step solution

01

Understanding the Problem

You are asked to simplify the expression \(12^2\). This means that you need to calculate what \(12\) squared is equal to.
02

Recognizing the Exponent

The exponent \(^2\) means that the base number, 12, is multiplied by itself. Therefore, you need to find the product of \(12 \times 12\).
03

Performing the Multiplication

Now, multiply 12 by itself: \(12 \times 12 = 144\).
04

Conclusion

The simplified form of the expression \(12^2\) is 144.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Squaring Numbers
Squaring a number is a straightforward concept in mathematics that involves multiplying a number by itself. When you see a number with an exponent of 2, like in \(12^2\), it tells you to perform this multiplication. In this exercise, the base number is 12.

Imagine you are asked to find 12 squared. This is simply establishing the product of 12 and 12.
  • 12 multiplied by 12 remains in the realm of basic arithmetic, yet it demonstrates the power of exponents beautifully.
  • The result, once calculated, is 144.
Recognizing this operation as squaring helps students see the symmetry and simplicity in multiplying a number by itself.
Multiplication
Multiplication is a fundamental operation in mathematics that is used across numerous problems and equations. At its core, multiplication is repeated addition. For instance, when multiplying 12 by 12, you are effectively adding the number 12 to itself 12 times.

Let's break it down:
  • The expression \(12 \times 12\) means adding 12 as a "chunk" 12 individual times: 12 + 12 + 12 + ... (and so on, 12 times).
  • When calculating \(12 \times 12\), it's common to set up the numbers in a simple column method where each digit of the second number multiplies accordingly.
This concept is easily manageable with practice and is essential for understanding how numbers grow and interact with each other through various operations.
Simplification of Expressions
Simplifying an expression involves reducing it to its most basic form. This makes problems easier to understand and solve. In algebraic simplification, you apply arithmetic operations to reduce an expression without changing its value.

Here, when we simplify \(12^2\), we are removing any unnecessary parts like the exponent and replacing it with its value, 144.
  • This step involves ensuring all operations are correctly applied and all numbers involved are reduced to as simple a state as possible.
  • Achieving a simplified answer means you have correctly followed and understood each arithmetic operation involved.
Simplification is a key skill, as it is used not only in basic arithmetic but also in complex equations across various fields of mathematics.

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