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Chapter 5: Problem 4

Evaluate each expression \(\sqrt{49}\)

Short Answer

Expert verified
The square root of 49 is 7.

Step by step solution

01

Calculate square root

The goal is to find a number, which gives 49 when it is multiplied by itself. As we know that \(7 \times 7 = 49\), so, the square root of 49 is 7.

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Key Concepts

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

Perfect Squares
Perfect squares are numbers that can be expressed as the product of an integer with itself. In simpler terms, a perfect square is like a magic number resulting from squaring an integer. For instance, when you take number 5 and multiply it by itself, you get 25, which makes 25 a perfect square. Understanding perfect squares helps simplify the process of finding square roots, as they are essentially the reverse operation. In the given exercise, 49 is a perfect square because it can be expressed as 7 times 7. Recognizing perfect squares allows you to quickly identify the square roots of these numbers.
Multiplication
Multiplication is one of the four fundamental operations in arithmetic, alongside addition, subtraction, and division. It involves combining equal groups to find a total quantity. Imagine you have 7 groups of 7 apples. Multiplying 7 by 7 gives you 49 apples in total. This operation is crucial when dealing with perfect squares because it allows us to determine which integer, when multiplied by itself, results in a given perfect square. Multiplication serves as the building block for finding square roots, as reversing this operation helps in breaking down perfect squares, such as finding that 7 times 7 equals 49.
Mathematical Expressions
A mathematical expression is a combination of numbers, symbols, and operators (like addition or multiplication) that together show a mathematical fact or idea. Expressions can be simple, like 2 + 3, or involve complex operations, such as \(\sqrt{49}\). In our context, the mathematical expression involves finding the square root of 49. Understanding how to read and evaluate these expressions is essential for solving many math problems. It involves breaking down the expression into simpler parts that are easier to understand and work with, like identifying a perfect square in the root expression.
Step-by-Step Solution
A step-by-step solution helps break down a complex problem into manageable parts, making it easier to solve. In tackling \(\sqrt{49}\), the step-by-step approach is:
  • Identify if the number is a perfect square.
  • Recall or determine which integer multiplied by itself gives the number (49 in this case).
  • Conclude the square root operation based on the multiplication.
In this case, recognizing 49 as a perfect square simplifies the process. Since 7 multiplied by 7 results in 49, deducing the square root is straightforward. By using a step-by-step method, solving expressions becomes a logical path to the solution, ensuring no steps are missed and understanding is reinforced.

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Most popular questions from this chapter

Use the appropriate formula shown above to find \(2+4+6+8+\cdots+200\), the sum of the first 100 positive even integers.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{4}\), when \(a_{1}=4, r=-3\).

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(3,12,48,192, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=4, r=2\)
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