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Chapter 8: Problem 11

Fill in the blanks. The symbol \(\sqrt{ }\) is called a _________ sign.

Short Answer

Expert verified
The symbol \(\sqrt{ }\) is called a square root sign.

Step by step solution

01

Identify the symbol

The symbol in question is a square root symbol. It is used in mathematics to indicate that we should find a number, which, when multiplied by itself, gives the number inside the symbol.
02

Fill in the blank

The statement then reads: 'The symbol \(\sqrt{ }\) is called a square root sign.'

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Key Concepts

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

Symbols in Algebra
In algebra, symbols play a crucial role as they represent numbers, operations, or relationships between quantities. One common symbol is the square root symbol, denoted as \( \sqrt{ } \). It indicates the operation of finding the square root of a number.
Algebra relies on many such symbols to simplify expressions and communicate complex ideas succinctly.
  • Variables are usually denoted by letters like \( x \), \( y \), and \( z \).
  • Operators include symbols like \( + \), \( - \), \( \times \), and \( \div \).
  • Functions, such as \( \sin \) for sine, are also crucial symbols in algebra.
Understanding these symbols is fundamental for solving equations and performing calculations.
Mathematical Notation
Mathematical notation is a system used to express mathematical ideas, concepts, and processes. Notation provides a universal language that mathematicians use for collaboration and communication. The square root, represented by \( \sqrt{ } \), is a standard part of this notation.
Mathematical notation consists of:
  • Symbols: Represent numbers and operations, like \( + \) for addition.
  • Numbers and Variables: Use both numbers like 2, 3, 4, and variables like \( x \) and \( y \).
  • Special Constants and Functions: Include items such as \( \pi \) for Pi and \( e \) for Euler's number.
These notations work together to clarify how mathematical processes are carried out.
Square Root Calculation
The concept of squaring a number involves multiplying it by itself. Conversely, the square root finds the original number that was squared. If \( n^2 = x \), then the square root of \( x \), denoted \( \sqrt{x} \), equals \( n \).
Calculating square roots can be done using:
  • Estimation: Finding a number close to the square root.
  • Prime factorization: Breaking down a number into its prime factors to find the square root.
  • Using a calculator: Most modern calculators have a square root function.
Square roots are essential for solving quadratic equations and other expressions in algebra. Understanding this concept helps in deciphering the relationships in mathematical problems.

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Most popular questions from this chapter

Simplify each expression. Assume that all variables represent positive values. Assume no division by 0. SEE EXAMPLE 6. (OBJECTIVE 3) $$\left(\frac{1}{1,000}\right)^{1 / 3}$$

Simplify. Assume that all variables in the radicand of an even root represent positive values. Assume no division by 0. Express each answer with positive exponents only. $$\left(-\frac{1}{32}\right)^{1 / 5}$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$\frac{1}{5} x^{2} y \sqrt{50 x^{2} y^{2}}$$

Simplify. All variables in square root problems represent positive values. Assume no division by 0. $$(\sqrt{5 x}+3 \sqrt{y})(\sqrt{5 x}-3 \sqrt{y})$$

Simplify each expression. All variables of square root expressions represent positive numbers. Assume no division by 0. $$-\frac{2}{5} \sqrt{80 m n^{2}}$$
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