Simplify The Square Root Of 108 In 3 Easy Steps

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Simplifying square roots is a fundamental concept in mathematics, and it's essential to have a solid grasp of this skill, especially when dealing with more complex problems. In this article, we'll break down the process of simplifying the square root of 108 into three easy steps. By the end of this explanation, you'll be able to simplify the square root of 108 with ease.

Why Simplify Square Roots?

Before we dive into the process of simplifying the square root of 108, it's essential to understand why we need to simplify square roots in the first place. Simplifying square roots helps us to:

• Write numbers in a more compact form
• Perform calculations more efficiently
• Solve problems with more accuracy

Step 1: Find the Factors of 108

To simplify the square root of 108, we need to start by finding the factors of 108. Factors are numbers that divide another number exactly without leaving a remainder. The factors of 108 are:

• 1
• 2
• 3
• 4
• 6
• 9
• 12
• 18
• 27
• 36
• 54
• 108

Identify the Perfect Square Factors

From the list of factors, we need to identify the perfect square factors. Perfect square factors are factors that are perfect squares themselves. In this case, the perfect square factors of 108 are:

• 1 (1²)
• 4 (2²)
• 9 (3²)
• 36 (6²)

Step 2: Write the Square Root of 108 as a Product of Factors

Now that we have identified the perfect square factors, we can write the square root of 108 as a product of these factors:

√108 = √(36 × 3)

Use the Property of Square Roots

Using the property of square roots, we can rewrite the expression as:

√108 = √36 × √3

Step 3: Simplify the Square Root of 108

Finally, we can simplify the square root of 108 by evaluating the square root of 36 and multiplying it by the square root of 3:

√108 = 6√3

And that's it! By following these three easy steps, we have simplified the square root of 108.

Key Takeaways

To recap, the key takeaways from this article are:

• Simplifying square roots is essential for mathematical calculations
• To simplify the square root of 108, we need to find the factors of 108 and identify the perfect square factors
• We can write the square root of 108 as a product of factors and use the property of square roots to simplify it

Conclusion

Simplifying the square root of 108 is a straightforward process that requires just three easy steps. By following these steps, you'll be able to simplify the square root of 108 and tackle more complex mathematical problems with confidence. Remember to practice regularly to reinforce your understanding of simplifying square roots.

We hope you found this article informative and helpful. If you have any questions or need further clarification, please don't hesitate to ask. Share your thoughts and feedback in the comments section below, and don't forget to share this article with your friends and colleagues who may benefit from it.