Problem 28 - Elementary Algebra

Question

\(7^{2}\)

Step-by-Step Solution

Answer

The value of \(7^2\) is 49.

Step 1: Understand the Exercise

The exercise asks for the value of the expression \(7^2\). This means we need to multiply the number 7 by itself.

Step 2: Perform the Calculation

Calculate \(7 \times 7\). Multiplying these two numbers gives \(49\).

Step 3: Write the Answer

The value of \(7^2\) is \(49\).

Key Concepts

Squared Number

A squared number is the result of multiplying a number by itself. For example, when you see an expression like \(7^2\), it means you need to multiply 7 by 7.
This operation is essential in many areas of mathematics, such as geometry and algebra.
A few more examples of squared numbers include:

• \(5^2 = 25\)
• \(3^2 = 9\)
• \(10^2 = 100\)

Squaring helps in finding the area of squares when you know the length of one side.
It is also a stepping stone to understanding higher powers of numbers.

Multiplication

Multiplication is one of the basic arithmetic operations. It involves adding a number to itself a certain number of times.
For instance, when you perform \(7 \times 7\), you're effectively adding 7 to itself seven times:
\[7 + 7 + 7 + 7 + 7 + 7 + 7 = 49\]
In the context of exponentiation, multiplication is used to compute powers such as \(7^2\).
Multiplication is a fundamental skill that is necessary for solving a range of mathematical problems.

When multiplying numbers, it's helpful to remember the multiplication facts for quick calculations.
Here are a few examples:

• \(2 \times 3 = 6\)
• \(4 \times 5 = 20\)
• \(6 \times 8 = 48\)

Powers of Numbers

Powers of numbers are expressions where a number is multiplied by itself a certain number of times.
The expression is written as \(a^b\), where \(a\) is the base and \(b\) is the exponent.
This notation signifies how many times the base number is multiplied by itself.
In the case of \(7^2\), the base is 7 and the exponent is 2, so \(7\) is multiplied by itself once.
Here are some more examples to illustrate:

• \(3^4 = 3 \times 3 \times 3 \times 3 = 81\)
• \(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\)
• \(5^3 = 5 \times 5 \times 5 = 125\)

Understanding powers is crucial in algebra and higher-level math topics.
They simplify the expression and handling of large numbers in calculations.