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Chapter 8: Problem 34

Simplify the squares and square roots. $$10^{2}$$

Short Answer

Expert verified
The simplified form of \(10^2\) is 100.

Step by step solution

01

- Understand the Problem

Recognize that you need to simplify the expression involving an exponentiated number.
02

- Apply the Exponent Rule

Remember that the notation for squaring a number is raising it to the power of 2. Hence, we will compute \(10^2\).
03

- Compute the Square

Calculate the value of \(10^2\) by multiplying 10 by itself: \(10 \times 10 = 100\).

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Key Concepts

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

squares in mathematics
In mathematics, when we talk about squares, we're referring to the result of multiplying a number by itself. This operation is also known as raising a number to the power of 2. For example, to find the square of 10, we write it as \(10^{2}\) which equals 10 multiplied by 10. The square of 10 is therefore 100. Squaring is a specific case of using exponents where the exponent is always 2. This is why we sometimes use the term 'squares' to specifically describe this operation. Squares are commonly used in various mathematical fields including geometry, algebra, and even in daily life for calculations related to area.
exponent rules
Exponent rules are guidelines that help us simplify expressions involving powers of numbers. Here are some essential rules:
  • The Product Rule: When multiplying two powers with the same base, you add the exponents, e.g. \(a^m \times a^n = a^{m+n}\).
  • The Power Rule: When raising a power to another power, you multiply the exponents, e.g. \( (a^m)^n = a^{mn} \).
  • The Zero Exponent Rule: Any base raised to the power of zero is 1, e.g. \(a^0 = 1\).
  • The Negative Exponent Rule: A negative exponent indicates taking the reciprocal of the base, e.g. \(a^{-n} = \frac{1}{a^n}\).
In our example, we used the understanding that \(10^2\) means multiplying 10 by itself. So, applying these exponent rules becomes straightforward with practice.
basic arithmetic operations
Basic arithmetic operations form the foundation of all mathematical calculations. They include addition, subtraction, multiplication, and division. Each of these operations has specific rules. Here's a quick rundown:
  • Addition: Combining two numbers to get a sum, e.g. \(5 + 3 = 8\).
  • Subtraction: Finding the difference between two numbers, e.g. \(5 - 3 = 2\).
  • Multiplication: Calculating the product of two numbers, e.g. \(4 \times 2 = 8\).
  • Division: Splitting a number into equal parts, e.g. \(8 \div 2 = 4\).
In our exercise, we used multiplication, one of the basic arithmetic operations, to square the number 10. This straightforward multiplication lets us understand squaring as an application of basic arithmetic.

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