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Chapter 7: Problem 105

Explain how to write the negative square root of a number using radical notation.

Short Answer

Expert verified
The negative square root of a number \(\backslashtext{a}\) is written as \(-\backslashsqrt{a}\).

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 is written as \(\backslashsqrt{}\).
02

Identify the Negative Square Root

The negative square root is simply the negative value of the positive square root. If \(\backslashsqrt{a}\) is the positive square root of \(\backslashtext{a}\), then \(-\backslashsqrt{a}\) represents the negative square root.
03

Write in Radical Notation

To write the negative square root of a number \(\backslashtext{a}\) in radical notation, place the radical symbol in front of the number, with a negative sign preceding it. It is written as: \(-\backslashsqrt{a}\). For example, the negative square root of 9 is written as \(-\backslashsqrt{9}\).

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Key Concepts

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

Radical Notation
Radical notation is a way to represent roots, particularly square roots, using the radical symbol \( \sqrt{} \).
The concept of radical notation helps in understanding how to express root values efficiently without long expressions.
In this system, the value inside the radical symbol, known as the radicand, is the number we want the root of.
For instance, \( \sqrt{16} \) represents the square root of 16.
This method is not limited to square roots alone and extends to higher-order roots using index numbers, like cube roots \( \sqrt[3]{8} \).
Square Root
The square root of a number is a value that, when multiplied by itself, equals the original number.
For example, the square root of 25 is 5, because \( 5 \times 5 = 25 \).
The square root is often represented by the radical symbol \( \sqrt{} \).
A square root can be either positive or negative, but we usually refer to the positive root when we say 'square root'.
To symbolize the negative square root, we place a negative sign before the radical symbol.
For example, the negative square root of 25 is written as \( -\sqrt{25} = -5 \).
Mathematical Notation
Mathematical notation refers to the symbols and signs used to represent numbers and operations.
It includes numbers, operators like addition or multiplication, and specific symbols like the radical to represent roots.
Using consistent notation helps in communication and understanding of mathematical ideas.
For example, \( +, -, \times, \div \) are basic mathematical operators we often use, while \( \sqrt{} \) is used for roots.
The proper use of notation ensures clarity and precision, which is crucial in problem-solving and mathematical expression.

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Most popular questions from this chapter

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. Write the answer using radical notation. $$ \frac{\sqrt{(7-y)^{3}}}{\sqrt[3]{(7-y)^{2}}} $$

Simplify. $$ \frac{1}{4+\sqrt{3}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}-4} $$

Factor completely. $$t^{3}+1000$$

Nadif incorrectly writes $$ \sqrt[5]{x^{2}} \cdot \sqrt{x^{3}}=x^{2 / 5} \cdot x^{3 / 2}=\sqrt[5]{x^{3}} $$ What mistake do you suspect he is making?

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. Write the answer using radical notation. $$ \frac{\sqrt[4]{x^{2} y^{3}}}{\sqrt[3]{x y}} $$
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