Simplify 128 Into Simplest Radical Form: 2 Easy Steps

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Simplifying radicals is an essential math skill that can seem daunting at first, but with the right approach, it can be made easy. In this article, we'll break down the process of simplifying the radical 128 into its simplest form using just two easy steps. By the end of this article, you'll have a solid understanding of how to simplify radicals and be able to tackle more complex problems with confidence.

The Importance of Simplifying Radicals

Radicals are used to represent the root of a number, and they are a crucial part of algebra and geometry. However, when working with radicals, it's essential to simplify them to their simplest form to make calculations easier and more efficient. Simplifying radicals also helps to avoid errors and ensures that you get the correct solution.

Step 1: Factor the Number Inside the Radical

To simplify the radical 128, we need to start by factoring the number inside the radical. This means breaking down 128 into its prime factors. The prime factorization of 128 is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

As you can see, 128 can be expressed as a product of 7 twos. This is the first step in simplifying the radical.

Step 2: Take Out the Perfect Squares

Now that we have factored 128 into its prime factors, we can take out the perfect squares. A perfect square is a number that can be expressed as the square of an integer. In this case, we can see that 128 can be expressed as:

128 = 64 × 2

Since 64 is a perfect square (8^2), we can take it out of the radical:

√128 = √(64 × 2) = 8√2

And there you have it! The simplified form of the radical 128 is 8√2.

Benefits of Simplifying Radicals

Simplifying radicals has several benefits, including:

• Easier calculations: Simplifying radicals makes calculations easier and more efficient.
• Avoiding errors: Simplifying radicals helps to avoid errors and ensures that you get the correct solution.
• Improved understanding: Simplifying radicals helps to improve your understanding of algebra and geometry.

Common Mistakes to Avoid

When simplifying radicals, there are several common mistakes to avoid, including:

• Not factoring the number inside the radical: Make sure to factor the number inside the radical to identify perfect squares.
• Not taking out perfect squares: Make sure to take out perfect squares to simplify the radical.
• Not checking for errors: Make sure to check your work for errors to ensure that you get the correct solution.

Conclusion

Simplifying radicals is an essential math skill that can seem daunting at first, but with the right approach, it can be made easy. By following the two easy steps outlined in this article, you can simplify the radical 128 into its simplest form. Remember to factor the number inside the radical and take out perfect squares to simplify the radical. With practice and patience, you'll become proficient in simplifying radicals and be able to tackle more complex problems with confidence.

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