Simplify 108: 3 Easy Steps To Radical Form

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Unlocking the Power of Simplifying 108: A Step-by-Step Guide

The concept of simplifying radicals is a fundamental aspect of mathematics, and understanding how to simplify 108 is essential for problem-solving and mathematical analysis. In this article, we will delve into the world of radical simplification, exploring the importance of this concept and providing a step-by-step guide on how to simplify 108.

Why Simplify Radicals?

Radicals, or roots, are mathematical expressions that involve the square root of a number. Simplifying radicals is crucial in various mathematical operations, such as addition, subtraction, multiplication, and division. By simplifying radicals, we can:

• Make mathematical calculations more manageable and efficient
• Enhance our understanding of mathematical concepts and relationships
• Improve problem-solving skills and accuracy

Step 1: Understanding the Radical Form of 108

The first step in simplifying 108 is to understand its radical form. The radical form of 108 can be expressed as √108. To simplify this expression, we need to find the factors of 108.

Prime Factorization of 108

To simplify the radical form of 108, we need to find its prime factors. The prime factorization of 108 is:

108 = 2 × 2 × 3 × 3 × 3

Step 2: Simplifying the Radical Form

Now that we have the prime factorization of 108, we can simplify the radical form. We can group the factors into pairs of identical factors:

√108 = √(2 × 2 × 3 × 3 × 3) = √(2^2 × 3^3) = 2 × 3√3 = 6√3

Why is 6√3 the Simplified Form?

The simplified form of √108 is 6√3 because we have factored out the perfect square (2^2) and the remaining factor (3) is left inside the square root. This simplification makes mathematical calculations more manageable and efficient.

Step 3: Verifying the Simplified Form

To verify the simplified form, we can multiply the factors:

6√3 = √(2^2 × 3^3) = √108

This verification confirms that the simplified form of √108 is indeed 6√3.

Real-World Applications of Simplifying Radicals

Simplifying radicals has numerous real-world applications, including:

• Physics and engineering: Simplifying radicals is essential in calculating distances, velocities, and accelerations.
• Computer science: Radicals are used in algorithms for solving equations and making predictions.
• Finance: Radicals are used in calculating interest rates, investments, and returns.

Conclusion: Simplifying 108 in 3 Easy Steps

In this article, we have explored the concept of simplifying radicals and provided a step-by-step guide on how to simplify 108. By following these three easy steps, you can simplify the radical form of 108 and enhance your problem-solving skills in mathematics.

Now that you have learned how to simplify 108, take the next step and practice simplifying other radicals. Remember to share your thoughts and feedback in the comments below.

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