Simplify 162 In Radical Form In 3 Easy Steps

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Simplifying radicals can be a daunting task for many, but with a clear step-by-step approach, it can become a manageable and even enjoyable process. In this article, we will delve into the world of radicals and explore how to simplify √162 in just three easy steps.

Understanding Radicals

Before we dive into the simplification process, it's essential to understand what radicals are and how they work. Radicals are mathematical expressions that represent the nth root of a number. In the case of √162, we are looking for the square root (nth root, where n = 2) of 162.

Step 1: Find the Largest Perfect Square

The first step in simplifying √162 is to find the largest perfect square that divides evenly into 162. A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is equal to 4^2.

To find the largest perfect square that divides into 162, we can start by listing the perfect squares less than or equal to 162:

• 1^2 = 1
• 2^2 = 4
• 3^2 = 9
• 4^2 = 16
• 5^2 = 25
• 6^2 = 36
• 7^2 = 49
• 8^2 = 64
• 9^2 = 81
• 10^2 = 100
• 11^2 = 121
• 12^2 = 144

From this list, we can see that the largest perfect square that divides into 162 is 81 (9^2).

Step 2: Divide the Number by the Perfect Square

Now that we have found the largest perfect square that divides into 162 (81), we can divide 162 by 81 to simplify the radical.

√162 = √(81 x 2)

Using the property of radicals that states √(ab) = √a x √b, we can rewrite the expression as:

√162 = √81 x √2

Step 3: Simplify the Radical

The final step is to simplify the radical by finding the square root of 81 and multiplying it by the square root of 2.

√81 = 9 (because 9^2 = 81)

So, we can rewrite the expression as:

√162 = 9√2

And that's it! We have successfully simplified √162 in just three easy steps.

Conclusion

Simplifying radicals can seem like a daunting task, but by breaking it down into manageable steps, we can make the process much more accessible. By understanding the properties of radicals and following the steps outlined in this article, you can simplify even the most complex radicals with ease.

So, what do you think? Do you have any questions or need further clarification on any of the steps? Leave a comment below, and let's continue the conversation!