Select All That Are Like Radicals To 11 \sqrt{11} 11 .- 6 11 3 6 \sqrt[3]{11} 6 3 11 - X 11 X \sqrt{11} X 11 - 2 11 3 2 \sqrt[3]{11} 2 3 11 - − 5 11 4 -5 \sqrt[4]{11} − 5 4 11 - − 6 11 -6 \sqrt{11} − 6 11

Mar 12, 2025 by ADMIN 217 views

**Selecting Like Radicals: A Comprehensive Guide**

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Understanding Like Radicals

When dealing with radicals, it's essential to understand the concept of like radicals. Like radicals are expressions that have the same index (or root) and the same radicand (the number inside the radical sign). In this article, we will explore how to select like radicals from a given set of expressions.

What are Like Radicals?

Like radicals are expressions that have the same index and radicand. For example, $\sqrt{11}$ and $x \sqrt{11}$ are like radicals because they have the same index (square root) and the same radicand (11). On the other hand, $\sqrt{11}$ and $\sqrt{12}$ are not like radicals because they have different radicands.

Selecting Like Radicals

To select like radicals, we need to identify the index and radicand of each expression. Let's take a look at the given expressions:

$6 \sqrt[3]{11}$
$x \sqrt{11}$
$2 \sqrt[3]{11}$
$-5 \sqrt[4]{11}$
$-6 \sqrt{11}$

Step 1: Identify the Index and Radicand

The first step is to identify the index and radicand of each expression.

$6 \sqrt[3]{11}$ : index = 3, radicand = 11
$x \sqrt{11}$ : index = 2, radicand = 11
$2 \sqrt[3]{11}$ : index = 3, radicand = 11
$-5 \sqrt[4]{11}$ : index = 4, radicand = 11
$-6 \sqrt{11}$ : index = 2, radicand = 11

Step 2: Select Like Radicals

Now that we have identified the index and radicand of each expression, we can select the like radicals.

$6 \sqrt[3]{11}$ and $2 \sqrt[3]{11}$ are like radicals because they have the same index (3) and the same radicand (11).
$x \sqrt{11}$ and $-6 \sqrt{11}$ are like radicals because they have the same index (2) and the same radicand (11).
$-5 \sqrt[4]{11}$ is not like any of the other expressions because it has a different index (4) and radicand (11).

Conclusion

Examples and Practice

Here are some examples and practice problems to help you understand like radicals better:

Select the like radicals from the following expressions: $\sqrt{11}$ , $x \sqrt{11}$ , $2 \sqrt[3]{11}$ , $-5 \sqrt[4]{11}$ , $-6 \sqrt{11}$ .
Select the like radicals from the following expressions: $\sqrt[3]{11}$ , $6 \sqrt[3]{11}$ , $x \sqrt{11}$ , $2 \sqrt[3]{11}$ , $-5 \sqrt[4]{11}$ .

Solutions

Here are the solutions to the examples and practice problems:

The like radicals from the expressions $\sqrt{11}$ , $x \sqrt{11}$ , $2 \sqrt[3]{11}$ , $-5 \sqrt[4]{11}$ , $-6 \sqrt{11}$ are $\sqrt{11}$ , $x \sqrt{11}$ , and $-6 \sqrt{11}$ .
The like radicals from the expressions $\sqrt[3]{11}$ , $6 \sqrt[3]{11}$ , $x \sqrt{11}$ , $2 \sqrt[3]{11}$ , $-5 \sqrt[4]{11}$ are $\sqrt[3]{11}$ , $6 \sqrt[3]{11}$ , and $2 \sqrt[3]{11}$ .

Tips and Tricks

Here are some tips and tricks to help you understand like radicals better:

Make sure to identify the index and radicand of each expression before selecting like radicals.
Compare the index and radicand of each expression to determine if they are like radicals.
Use the examples and practice problems to help you understand like radicals better.

Common Mistakes

Here are some common mistakes to avoid when selecting like radicals:

Not identifying the index and radicand of each expression.
Comparing the wrong index or radicand.
Not using the correct notation for like radicals.

Conclusion

In conclusion, like radicals are expressions that have the same index and radicand. To select like radicals, we need to identify the index and radicand of each expression and then compare them. By following these steps, we can easily select like radicals from a given set of expressions. Remember to use the examples and practice problems to help you understand like radicals better, and avoid common mistakes when selecting like radicals.

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Q: What are like radicals?

A: Like radicals are expressions that have the same index (or root) and the same radicand (the number inside the radical sign). For example, $\sqrt{11}$ and $x \sqrt{11}$ are like radicals because they have the same index (square root) and the same radicand (11).

Q: How do I identify like radicals?

A: To identify like radicals, you need to compare the index and radicand of each expression. If the index and radicand are the same, then the expressions are like radicals.

Q: What are some examples of like radicals?

A: Here are some examples of like radicals:

$\sqrt{11}$ and $x \sqrt{11}$ are like radicals because they have the same index (square root) and the same radicand (11).
$\sqrt[3]{11}$ and $6 \sqrt[3]{11}$ are like radicals because they have the same index (cube root) and the same radicand (11).
$\sqrt{11}$ and $-6 \sqrt{11}$ are like radicals because they have the same index (square root) and the same radicand (11).

Q: What are some examples of unlike radicals?

A: Here are some examples of unlike radicals:

$\sqrt{11}$ and $\sqrt{12}$ are unlike radicals because they have different radicands (11 and 12).
$\sqrt[3]{11}$ and $\sqrt[3]{12}$ are unlike radicals because they have different radicands (11 and 12).
$\sqrt{11}$ and $\sqrt[3]{11}$ are unlike radicals because they have different indices (square root and cube root).

Q: Can I add or subtract unlike radicals?

A: No, you cannot add or subtract unlike radicals. Unlike radicals have different indices or radicands, so they cannot be combined using addition or subtraction.

Q: Can I multiply or divide unlike radicals?

A: Yes, you can multiply or divide unlike radicals. However, you need to follow the rules of exponents when multiplying or dividing radicals.

Q: What are some common mistakes to avoid when working with like radicals?

A: Here are some common mistakes to avoid when working with like radicals:

Not identifying the index and radicand of each expression.
Comparing the wrong index or radicand.
Not using the correct notation for like radicals.
Adding or subtracting unlike radicals.

Q: How can I practice working with like radicals?

A: Here are some ways to practice working with like radicals:

Use online resources, such as math websites or apps, to practice identifying and working with like radicals.
Work with a tutor or teacher to practice identifying and working with like radicals.
Use real-world examples, such as measuring the length of a room or the area of a garden, to practice working with like radicals.

Q: What are some real-world applications of like radicals?

A: Here are some real-world applications of like radicals:

Measuring the length of a room or the area of a garden.
Calculating the volume of a cube or a rectangular prism.
Working with fractions and decimals in real-world applications, such as cooking or finance.

Q: Can I use like radicals to solve real-world problems?

A: Yes, you can use like radicals to solve real-world problems. Like radicals can be used to simplify complex expressions and make it easier to solve problems.

Q: What are some tips for working with like radicals?

A: Here are some tips for working with like radicals:

Make sure to identify the index and radicand of each expression before working with like radicals.
Use the correct notation for like radicals.
Practice working with like radicals to build your skills and confidence.
Use real-world examples to make working with like radicals more engaging and relevant.