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Chapter 7: Problem 20

Simplify. $$ -\sqrt{100} $$

Short Answer

Expert verified
-10

Step by step solution

01

Understand the square root

The square root of a number is a value that, when multiplied by itself, gives the original number. The square root symbol (鈭�) represents this operation.
02

Calculate the square root of 100

Identify the number that, when multiplied by itself, equals 100. The square root of 100 is 10 because \(10 \times 10 = 100\).
03

Apply the negative sign

Since the original problem is \(-\sqrt{100}\), you need to apply the negative sign to the square root value found in Step 2. Therefore, \(-\sqrt{100} = -10\).

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Key Concepts

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

The Concept of Square Roots
A square root refers to a number that, when multiplied by itself, yields the original number. It is represented by the symbol \( \sqrt{} \). For instance, the square root of 100 is 10 because \(10 \times 10 = 100\). To determine the square root of a number, you can look for a value that produces the original number when squared. This process simplifies complex numbers and is essential for various mathematical operations. Understanding square roots is vital, as it helps in solving equations and problems involving exponential values.
Negative Numbers
Negative numbers can be tricky. When you see a negative sign in front of the square root symbol, it means you need to find the negative value of the square root. For example, in the expression \( -\sqrt{100} \), you first find the square root of 100, which is 10. Then you apply the negative sign, making it -10. In essence, this operation transforms your result into its negative counterpart. Negative numbers are simply values that are less than zero and are represented with a minus sign (-). They are used in various real-world scenarios, like temperatures below freezing, or financial debts.
Multiplication Involved in Square Roots
To fully grasp square roots, you must understand multiplication. Multiplication involves combining equal groups of numbers. For square roots, you need to know which number multiplied by itself equals the given number. Consider \( \sqrt{100} \), which asks, 'What number times itself gives 100?' The answer is 10 because \(10 \times 10 = 100\). This is a fundamental property of square roots and highlights the critical relationship between multiplication and square roots. Mastering multiplication makes it easier to work with and simplify square roots effectively.

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Most popular questions from this chapter

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