Problem 32 Identify the radicand and the in... [FREE SOLUTION]

Chapter 10: Problem 32

Identify the radicand and the index for each expression. $$ \frac{a}{b} \sqrt[6]{a^{2}+1} $$

Short Answer

Expert verified

The radicand is $ a^{2} + 1 $ and the index is $ 6 $.

Step by step solution

Identify the Radicand

The radicand is the expression inside the radical symbol. For this problem, the expression inside the radical is $ a^{2} + 1 $. This means that the radicand is $ a^{2} + 1 $.

Identify the Index

The index is the small number written just outside and above the radical symbol which indicates the root being taken. In this problem, the index is $ 6 $, indicating a sixth root.

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Key Concepts

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

radicand

When dealing with radical expressions, one of the first things to identify is the radicand. This is simply the value or the expression inside the radical (or root) symbol. Imagine when you're working with a square root, for example, $\frac{a}{b} \times \sqrt[6]{a^{2}+1} $, what you see inside the radical symbol is the radicand. In our specific exercise, the radicand is identified as $ a^{2} + 1 $. Recognizing the radicand is crucial because it is what you are taking the root of. Make sure to always locate the radicand first before moving on to other parts of the radical expression.

index in radical expressions

The next key component of a radical expression is the index. The index tells you which root of the radicand you are taking. It is a small number positioned just outside and above the radical symbol. For example, in the expression $ \frac{a}{b} \sqrt[6]{a^{2}+1} $, the number 6 is the index. This means you are dealing with a sixth root of the radicand. In simpler terms, if the index is 2, you are finding the square root; if the index is 3, you are finding the cube root, and so on. The index is vital as it changes how you calculate the root of the radicand. Always identify the index to effectively understand and solve the radical expression properly.

sixth root

Among the variety of roots you can encounter, the sixth root is a bit less common but still important. In our exercise, we have $ \theta = \frac{a}{b} \sqrt[6]{a^{2}+1} $, which means we are finding the sixth root of $ a^{2} + 1 $. The sixth root of a number $ x $ is a number that, when multiplied by itself six times, gives $ x $. Mathematically, if $ y \sqrt[6]{x} = x^{1/6} $, then $ y^6 = x $. Understanding the specific root you are dealing with is important as it heavily influences your calculations. Employing this knowledge will make complex expressions more manageable and less intimidating.

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91影视

Identify the radicand and the index for each expression. $$ \frac{a}{b} \sqrt[6]{a^{2}+1} $$

Short Answer

Step by step solution

Identify the Radicand

Identify the Index

Key Concepts

radicand

index in radical expressions

sixth root

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