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Chapter 8: Problem 7

Quickly solve these square root problems. \(\sqrt{16}\)

Short Answer

Expert verified
4

Step by step solution

01

Identify the Number

Locate the number inside the square root. In this case, the number is 16.
02

Determine the Square Root

Find which number, when multiplied by itself, equals 16. Since 4 multiplied by 4 equals 16, the square root of 16 is 4.

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Key Concepts

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

headline of the respective core concept
Square roots are a foundational concept in mathematics, especially in algebra. They help in solving equations and understanding various geometrical concepts. The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, when we take the square root of 16, we are looking for a number which, multiplied by itself, results in 16. That number is 4 because \( 4 \times 4 = 16 \).

When solving square roots, it's important to remember:
  • The square root symbol is \( \sqrt{ } \).
  • Mental math or knowing perfect squares can speed up the process.
  • Using a calculator can help when dealing with non-perfect squares.
headline of the respective core concept
Step-by-step math solutions are excellent tools to grasp how to solve a problem in a structured manner. They break down the solution into manageable parts, making it easier to follow the logic behind each step.

For solving square roots step-by-step, consider the method used in our example:
1. Identify the number inside the square root, in this case, 16.
2. Determine which number multiplied by itself gives the original number. Here, 4 multiplied by 4 equals 16, so the square root of 16 is 4.

Breaking down problems in this systematic manner helps build a strong foundation in problem-solving skills and boosts confidence in handling more complex equations.
headline of the respective core concept
Basic algebra problems often involve finding unknown values and performing operations with variables. These problems can range from simple calculations to more complicated equations. Understanding how to handle square roots is a crucial part of more complex algebraic expressions.

Key points to remember in algebra are:
  • Simplify expressions by removing parentheses and combining like terms.
  • Use inverse operations to isolate variables when solving equations.
  • Understand and apply the properties of equality.
By mastering basic algebra, including operations with square roots, you lay a solid groundwork for all future math courses and applications.

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Most popular questions from this chapter

Solve. \(\sqrt{12} \sqrt{3}\)

Solve the following radicals. Be careful. Some of them are undefined. \(\sqrt[3]{-27}\)

Solve for \(x\). \(\sqrt[x]{125}=5\)

In each of the following, add or subtract the radical expressions. \(2 \sqrt{x}-2 \sqrt{x}\)

Solve each of the following square root problems by rewriting the radical expression as two separate expressions. \(\sqrt{(64)(100)}\)
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