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Chapter 8: Problem 99

What are like radicals? Give an example with your explanation.

Short Answer

Expert verified
'Like radicals' are radicals that have the same radicand and the same index. An example of like radicals could be \(\sqrt{3}\) and 2\(\sqrt{3}\), which can be combined to 3\(\sqrt{3}\).

Step by step solution

01

Defining Radicals

Radicals denote a root of a certain number or expression, which is usually indicated by the symbol 鈭� (a square root). For example, \(\sqrt{4}\) is a radical which refers to the square root of 4.
02

Explaining Like Radicals

Like radicals are radical terms that have the same radicand (number under the root) and the same index (the root itself). Therefore, like radicals can be combined or simplified.
03

Providing an Example

An example of like radicals could be \(\sqrt{3}\) and 2\(\sqrt{3}\). These are like radicals because they have the same radicand (3) and the same index (the square root). These like radicals can be combined into 3\(\sqrt{3}\).

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Most popular questions from this chapter

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{1}{4+\sqrt{3}}$$

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{2}{\sqrt{5}-\sqrt{3}}$$

Simplify by first writing the expression in radical form. If applicable, use a calculator to verify your answer. $$\left(\frac{1}{9}\right)^{-\frac{1}{2}}$$

Simplify by first writing the expression in radical form. If applicable, use a calculator to verify your answer. $$(-8)^{-\frac{2}{3}}$$

Simplify each expression. Write answers in exponential form with positive exponents only. Assume that all variables represent positive real numbers. $$x^{\frac{1}{3}} \cdot x^{\frac{1}{4}}$$
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