Simplify 108 Into Simplest Radical Form

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The square root of 108 can be simplified into simplest radical form.

Step 1: Factor 108 into Prime Numbers

To simplify the square root of 108, we need to factor 108 into its prime factors.

108 = 2 × 2 × 3 × 3 × 3

Step 2: Group the Prime Factors into Pairs

Now, we can group the prime factors into pairs.

108 = (2 × 2) × (3 × 3) × 3

Step 3: Take the Square Root of the Pairs

Taking the square root of the pairs, we get:

√108 = √(2 × 2) × √(3 × 3) × √3

√108 = 2 × 3 × √3

Simplified Radical Form

So, the simplified radical form of √108 is:

√108 = 6√3

In this form, the square root of 108 is simplified into simplest radical form.

Key Takeaways

• The square root of 108 can be simplified into simplest radical form.
• The prime factorization of 108 is 2 × 2 × 3 × 3 × 3.
• Grouping the prime factors into pairs, we get (2 × 2) × (3 × 3) × 3.
• Taking the square root of the pairs, we get 2 × 3 × √3.
• The simplified radical form of √108 is 6√3.

Additional Information

Simplifying square roots is an essential skill in mathematics, particularly in algebra and geometry. By breaking down numbers into their prime factors, we can simplify square roots and express them in simplest radical form.

Common Mistakes to Avoid

When simplifying square roots, it's essential to avoid common mistakes, such as:

• Not factoring the number into prime factors.
• Not grouping the prime factors correctly.
• Not taking the square root of the pairs correctly.

By following these steps and avoiding common mistakes, you can simplify square roots with confidence.

Practice Problems

Practice simplifying the following square roots:

• √48
• √75
• √120

Remember to factor the numbers into prime factors, group the prime factors into pairs, and take the square root of the pairs.

Conclusion

Simplifying the square root of 108 is a straightforward process that involves factoring the number into prime factors, grouping the prime factors into pairs, and taking the square root of the pairs. By following these steps, you can simplify the square root of 108 and express it in simplest radical form.

If you have any questions or need further clarification, feel free to ask in the comments below. Share this article with your friends and classmates who may benefit from it.