Simplify Square Root Of 216

Square Root of 216 How to Find the Square Root of 216? from www.cuemath.com

Introduction

Square roots are one of the fundamental concepts of mathematics. They are used in various fields like engineering, physics, and architecture. Simplifying square roots is a crucial aspect of mathematics because they are often involved in complex calculations. In this article, we will discuss how to simplify the square root of 216.

What is Square Root?

In mathematics, the 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 is equal to 16. The symbol used to represent the square root is √.

What is Simplifying Square Root?

Simplifying square roots means finding the simplest form of the square root. In other words, we want to express the square root in terms of its factors, such that there is no perfect square left inside the radical. The simplest form of a square root is when the number inside the radical has been broken down into its prime factors.

What is 216?

216 is a composite number, which means it has more than two factors. The prime factors of 216 are 2, 3, and 3. Therefore, we can write 216 as 2 x 3 x 3 x 12.

How to Simplify the Square Root of 216?

To simplify the square root of 216, we need to break it down into its prime factors. We already know that the prime factors of 216 are 2, 3, and 3. We can group the prime factors in pairs, such that one factor from each pair is taken outside the radical, and the other factor remains inside the radical. Therefore, we can write the square root of 216 as √(2 x 3 x 3 x 12) = √(2 x 3 x 3) x √12.

Simplifying the Square Root of 12

To simplify the square root of 12, we need to break it down into its prime factors. The prime factors of 12 are 2 and 3. Therefore, we can write the square root of 12 as √(2 x 2 x 3) = 2√3.

Substituting the Value of √12

Now that we have simplified the square root of 12, we can substitute its value in the expression we got earlier. Therefore, the square root of 216 can be written as √(2 x 3 x 3) x 2√3.

Multiplying the Factors

Now, we can simplify this expression further by multiplying the factors inside the radical. Therefore, the square root of 216 can be written as 6√3.

Conclusion

In conclusion, we can say that simplifying square roots is a crucial aspect of mathematics. It helps us to express complex numbers in their simplest form. To simplify the square root of 216, we need to break it down into its prime factors and group them in pairs. We can then simplify the expression further by substituting the value of the square root of 12 and multiplying the factors inside the radical.