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Chapter 2: Problem 58

Simplify. \(3^{2}+7^{2}\)

Short Answer

Expert verified
58

Step by step solution

01

Identify Each Base

Identify the bases in the given expression. The bases are 3 and 7.
02

Square Each Base

Square each of the bases: Calculate 3 squared: 3^{2} = 9 Calculate 7 squared: 7^{2}=49
03

Add the Results

Add the two results from squaring the bases: 9 + 49 = 58

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Key Concepts

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

Exponents
Exponents are a way to express repeated multiplication of the same number. When you see a number with an exponent, like 3^2, it means you multiply 3 by itself.

For example:
  • 3^2 = 3 * 3
  • 7^2 = 7 * 7

So, 3^2 = 9 and 7^2 = 49. Understanding exponents makes it easier to work with numbers and simplify expressions.
Addition
Addition is one of the basic operations in mathematics. It's the process of combining two or more numbers to get a total.

For instance, in the expression given, after we squared 3 and 7, we got 9 and 49 respectively. To simplify the overall expression, we need to add these two results:
  • 9 + 49 = 58

This step is straightforward: you start from the rightmost digit and work your way left, carrying over any extra value to the next column if needed. Combining results through addition is critical for simplifying expressions like the one given.
Powers of Numbers
Powers of numbers are another way to express numbers raised to an exponent. When dealing with powers, it's crucial to understand the base and the exponent.

The base is the number you're multiplying, and the exponent tells you how many times to multiply it. In the expression provided: 3^2 and 7^2, 3 and 7 are the bases, and 2 is the exponent for both.
Key points to remember:
  • 3^2 is read as 'three squared' and means 3 * 3 = 9
  • 7^2 is read as 'seven squared' and means 7 * 7 = 49

These fundamentals of exponents and powers help in simplifying and understanding mathematical expressions.

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