Problem 55 Identify the radicand and the in... [FREE SOLUTION]

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Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 7: Problem 55

Identify the radicand and the index for each expression. $$ 5 \sqrt{p^{2}+4} $$

Short Answer

Expert verified

Radicand: $p^2 + 4$, Index: 2

Step by step solution

- Understanding the expression

Break down the given expression, which is $5 \sqrt{p^{2}+4}$. This expression consists of a constant (5), a square root symbol (\sqrt{}), and the term inside the square root symbol, which is $p^2 + 4$.

- Identifying the radicand

The radicand is the term inside the square root symbol. For the given expression, the radicand is $p^2 + 4$.

- Identifying the index

The index of a radical specifies the degree of the root. The index is usually written as a small number to the upper left of the radical sign. When no index is written, it is assumed to be 2 (indicating a square root). For $5 \sqrt{p^2 + 4} $, the index is 2.

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Key Concepts

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

Radicand

In algebra, the radicand is a key concept when dealing with radicals. It is the term or the expression inside the radical (鈭�) symbol.

This is what you are trying to find the root of.
For example, in the expression $5 \sqrt{p^2 + 4}$, the radicand is $p^2 + 4$.

The radicand can be a single number, a variable, or a combination of both like $p^2 + 4$. Understanding the radicand is essential for solving radical equations and simplifying radical expressions.

Index of a Radical

The index of a radical shows the degree of the root you are taking. It is typically written as a small number to the upper left of the radical symbol (鈭�).

If there鈥檚 no number, it鈥檚 assumed to be 2, which means it鈥檚 a square root.
In the expression $5 \sqrt{p^2 + 4}$, the index is 2 because no number is mentioned.

Remember, the index can be any positive integer and it indicates:

2 for a square root
3 for a cube root
4 for a fourth root, and so on

By knowing the index, you understand the type of root you are working with in your calculations.

Square Root

A square root is a type of radical where the index is 2. It means finding a number that, when multiplied by itself, gives the original number (the radicand).

In algebraic form, the square root of a number $x$ is written as $\sqrt{x}$.
For example, $\sqrt{16} = 4$ because $4 \times 4 = 16$.

In the given expression $5 \sqrt{p^2 + 4}$, the radicand $p^2 + 4$ is under a square root. Knowing how to work with square roots is fundamental for simplifying expressions and solving equations in algebra.

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91影视

Identify the radicand and the index for each expression. $$ 5 \sqrt{p^{2}+4} $$

Short Answer

Step by step solution

- Understanding the expression

- Identifying the radicand

- Identifying the index

Key Concepts

Radicand

Index of a Radical

Square Root

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