Simplifying Radicals Worksheet 1 Answers

Okay, so you’ve tackled Simplifying Radicals Worksheet 1, and you’re looking for the answers. You’re not alone! Simplifying radicals can be tricky, especially when you’re just starting out. It involves breaking down numbers under a square root (or cube root, etc.) into their prime factors and then pulling out any perfect squares (or cubes, etc.). It’s a foundational skill in algebra and vital for more advanced math courses. This post will provide you with the answers to a typical Simplifying Radicals Worksheet 1, and we’ll also briefly touch on the concepts involved to help solidify your understanding.

Before diving into the answers, let’s quickly review the key concept: simplifying radicals. The goal is to express a radical in its simplest form. A radical is considered simplified when the radicand (the number under the radical symbol) has no perfect square factors (other than 1). For example, √8 can be simplified because 8 has a perfect square factor of 4. We can rewrite √8 as √(4 * 2), which then becomes √4 * √2, and finally, 2√2. The simplified form is 2√2 because the number under the radical (2) no longer has any perfect square factors.

The process generally involves these steps:

Find the prime factorization of the radicand: Break down the number under the radical into its prime factors.
Identify perfect square factors: Look for pairs of identical prime factors. Remember that √x * √x = x.
Pull out the perfect squares: For each pair of identical prime factors, bring one of those factors outside the radical.
Simplify: Multiply any numbers outside the radical together and any remaining factors under the radical together.

Consider the example √72. First, find the prime factorization: 72 = 2 x 2 x 2 x 3 x 3. We have a pair of 2s and a pair of 3s. This allows us to rewrite √72 as √(2² * 3² * 2). Then, we pull out the 2 and the 3, leaving us with 2 * 3 * √2, which simplifies to 6√2. Therefore, √72 simplified is 6√2.

Understanding these steps will make simplifying radicals much easier. Now, let’s get to the answers. Remember to check your work carefully and understand *why* the answer is what it is, not just memorize the answers.

Below are the answers to a typical Simplifying Radicals Worksheet 1. Please note that your worksheet may contain different problems, but the process for solving them will be the same. We will assume the worksheet focused on square roots.

Worksheet 1 – Answers

1) √20 = 2√5
2) √48 = 4√3
3) √75 = 5√3
4) √12 = 2√3
5) √32 = 4√2
6) √50 = 5√2
7) √18 = 3√2
8) √27 = 3√3
9) √80 = 4√5
10) √98 = 7√2
11) √125 = 5√5
12) √200 = 10√2
13) √363 = 11√3
14) √432 = 12√3
15) √605 = 11√5

Hopefully, you found those answers helpful! Remember, practice makes perfect. The more you work with simplifying radicals, the easier it will become. If you’re still struggling, consider looking for additional resources online, such as videos or interactive tutorials. Also, don’t hesitate to ask your teacher or a classmate for help. Math is a collaborative effort, and learning from others can be incredibly beneficial.

Keep practicing, and you’ll master simplifying radicals in no time! Good luck!

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