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Chapter 8: Problem 96

Explain the meaning of the words radical, radicand, and index. Give an example with your explanation.

Short Answer

Expert verified
The radical is the '鈭�' symbol, the radicand is the value under the radical symbol (to which the root operation is applied), and the index is the degree of the root being taken, where a non-displayed index implies a square root.

Step by step solution

01

Explanation of Radical

The term 'Radical' in mathematics is used to describe a symbol that represents the operation of root extraction. This symbol is often written as 鈭�. For example, in the expression 鈭�9, the '鈭�' is the radical signifier.
02

Explanation of Radicand

The term 'Radicand' refers to the number or expression underneath a radical symbol, the value that the root operation is applied to. In the example 鈭�9, the number 9 is the radicand.
03

Explanation of Index

The 'Index' represents the degree of the root being taken. When the index is not shown, a square root is implied. In a square root operation like 鈭�9, the index is 2 (even though it's not shown). For a cube root operation such as \(\sqrt[3]{8}\), the index is 3.

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Most popular questions from this chapter

Simplify by first writing the expression in radical form. If applicable, use a calculator to verify your answer. $$81^{-\frac{5}{4}}$$

In Exercises \(75-82\), rationalize each denominator. Simplify, if possible $$\frac{\sqrt{2}}{\sqrt{7}}+\frac{\sqrt{7}}{\sqrt{2}}$$

Simplify: \(\frac{(2 x)^{5}}{x^{3}} .\) (Section 5.7, Example 5)

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{8}{\sqrt{7}+\sqrt{3}}$$

Square the real number \(\frac{2}{\sqrt{3}} .\) Observe that the radical is eliminated from the denominator. Explain whether this process is equivalent to rationalizing the denominator.
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