3 Steps To Simplify Square Root Of 84

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Mastering the art of simplifying square roots is an essential skill in mathematics, and it can be a game-changer for students and professionals alike. One of the most common square roots that people struggle with is the square root of 84. In this article, we will break down the steps to simplify the square root of 84, making it easier for you to tackle even the most complex math problems.

The importance of simplifying square roots cannot be overstated. By simplifying square roots, you can make calculations easier, reduce errors, and improve your overall understanding of mathematical concepts. In this article, we will focus on the square root of 84, but the techniques we cover can be applied to any square root.

Understanding Square Roots

Before we dive into the steps to simplify the square root of 84, let's take a moment to understand what square roots are. A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

What is the Square Root of 84?

The square root of 84 is a value that, when multiplied by itself, gives 84. However, the square root of 84 is not a whole number, which is why we need to simplify it.

Step 1: Factorize the Number

To simplify the square root of 84, we need to factorize the number 84. Factorizing a number means breaking it down into its prime factors. The prime factors of 84 are 2, 2, 3, and 7.

Prime Factors of 84

The prime factors of 84 are:

• 2 (appears twice)
• 3
• 7

Step 2: Group the Prime Factors

Now that we have the prime factors of 84, we need to group them in pairs. We can group the two 2's together, and the 3 and 7 will remain as separate factors.

Grouped Prime Factors of 84

The grouped prime factors of 84 are:

• 2 x 2
• 3
• 7

Step 3: Simplify the Square Root

Now that we have the grouped prime factors of 84, we can simplify the square root. We can take the square root of the paired factors (2 x 2), which gives us 2 times the square root of 3 times the square root of 7.

Simplified Square Root of 84

The simplified square root of 84 is:

2√(3 x 7)

Or:

2√21

Conclusion

Simplifying the square root of 84 may seem daunting at first, but by following these three steps, you can break it down into a manageable problem. Remember to factorize the number, group the prime factors, and simplify the square root. With practice, you'll become a pro at simplifying square roots in no time!

Now, it's your turn! Take a moment to practice simplifying the square root of 84 using the steps outlined above. Share your results in the comments below, and don't hesitate to ask if you have any questions.