Simplifying Square Root Of 128

Square Root of 128 in Simplest Radical Form from marissa-blogcervantes.blogspot.com

Introduction

Square roots are an essential part of mathematics, and they are used to find the value of the square root of a number. Simplifying the square root of a number means finding the smallest possible value that can be obtained. In this article, we will discuss how to simplify the square root of 128.

What is a Square Root?

A square root is a mathematical operation that gives the value of a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9.

How to Simplify the Square Root of 128

To simplify the square root of 128, we need to find the factors of 128. This can be done by dividing 128 by its prime factors. The prime factors of 128 are 2, 2, 2, 2, 2, and 2. Therefore, we can write 128 as 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2.

Step 1: Group the Factors

We can group the factors into pairs of two as follows: 2 x 2 = 4 4 x 2 = 8 8 x 2 = 16 16 x 2 = 32 32 x 2 = 64 64 x 2 = 128

Step 2: Simplify the Square Root

We can now simplify the square root of 128 using the factors we have found. We can write the square root of 128 as the square root of (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2) which is equal to the square root of (2 x 2 x 2 x 2) multiplied by the square root of (2 x 2 x 2 x 2 x 2 x 2).

Step 3: Simplify Further

The square root of (2 x 2 x 2 x 2) is equal to 4, and the square root of (2 x 2 x 2 x 2 x 2 x 2) is equal to 8. Therefore, we can write the square root of 128 as 4 x 8, which is equal to 32.

Conclusion

Simplifying the square root of 128 involves finding the prime factors of 128, grouping the factors into pairs of two, simplifying the square root using the factors, and simplifying further to obtain the smallest possible value. The simplified value of the square root of 128 is 32.