Simplifying Square Root Of 192

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

Introduction

Square roots are a fundamental concept in mathematics, and they are used in many areas such as engineering, physics, and geometry. Simplifying square roots is a common task in algebra, and it involves finding the largest perfect square that divides a given number. In this article, we will discuss how to simplify the square root of 192.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3x3=9. The symbol used to represent a square root is √. The number under the symbol is called the radicand.

Simplifying Square Roots

To simplify a square root, we need to find the largest perfect square that divides the radicand. A perfect square is a number that is the product of an integer multiplied by itself. For example, 9, 16, and 25 are perfect squares because they are the products of 3x3, 4x4, and 5x5, respectively.

Simplifying Square Root of 192

To simplify the square root of 192, we need to find the largest perfect square that divides 192. We can do this by factoring 192 into its prime factors: 192 = 2 x 2 x 2 x 2 x 2 x 3 We can see that 16 is the largest perfect square that divides 192. Therefore, we can simplify the square root of 192 as follows: √192 = √(16 x 12) = √16 x √12 = 4√12

Further Simplification

We can simplify the square root of 12 by factoring it into its prime factors: 12 = 2 x 2 x 3 Therefore, we can simplify 4√12 as follows: 4√12 = 4 x √(2 x 2 x 3) = 4 x √2 x √2 x √3 = 4 x 2√3 = 8√3

Conclusion

In conclusion, simplifying the square root of 192 involves factoring it into its prime factors and finding the largest perfect square that divides it. We can simplify the square root of 192 as 8√3. Simplifying square roots is an important skill in algebra, and it is useful in many practical applications.