Simplifying The Square Root Of 192

Square Root of 192 How to Find the Square Root of 192? Cuemath from www.cuemath.com

Introduction

As a professional teacher, I understand that students may find it challenging to simplify the square root of 192. However, with the right approach, it is possible to solve this problem with ease. In this article, I will explain the steps to simplify the square root of 192.

What is Square Root?

Before we dive into simplifying the square root of 192, let us first understand what square root is. A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, since 5 multiplied by itself gives 25.

The Steps to Simplify the Square Root of 192

To simplify the square root of 192, we need to find the factors of 192 that are perfect squares. Here are the steps to follow:

Step 1: Prime Factorization

The first step is to find the prime factorization of 192. We can do this by dividing 192 by the smallest prime number, which is 2. We keep dividing by 2 until we get an odd number. 192 ÷ 2 = 96 96 ÷ 2 = 48 48 ÷ 2 = 24 24 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷ 2 = 3 So the prime factorization of 192 is 2 x 2 x 2 x 2 x 2 x 3.

Step 2: Grouping Factors

The next step is to group the factors into pairs of two. We start with the first factor and pair it with another factor until we are left with one factor. 2 x 2 x 2 x 2 x 2 x 3 = (2 x 2) x (2 x 2) x 2 x 3

Step 3: Simplifying

Finally, we simplify the expression by taking the square root of the perfect squares in the expression. (2 x 2) x (2 x 2) x 2 x 3 = 16 x 2 x 3 The square root of 16 is 4, so we can simplify the expression further: 16 x 2 x 3 = 4 x 4 x 2 x 3 = 4 x (4 x 3 x 2) = 4 x 24 Therefore, the simplified square root of 192 is 4√24.

Conclusion

In conclusion, simplifying the square root of 192 requires finding the factors of 192 that are perfect squares, grouping them, and simplifying the expression. By following the steps outlined in this article, students can easily simplify the square root of 192 and other similar problems. As a teacher, I encourage students to practice solving more problems to improve their understanding of square roots.