When is Written in Simplest Radical Form: Exploring the Values Under the Radical

When expressing a number in its simplest radical form, it means simplifying the square root or cube root as much as possible. In this article, we will discuss the values under the radical when the number is written in its simplest radical form. We will explore the options of 3, 6, 9, and 27 and determine which value remains under the radical. Let's delve into the topic and gain a better understanding.

Getting radical into simplest radical form

1. Understanding Simplest Radical Form:

Before we dive into the specific values, let's understand what simplest radical form means.

In mathematics, expressing a number in simplest radical form involves removing any perfect square factors from the radical.

The goal is to simplify the expression as much as possible.

2. Evaluating the Values:

Now, let's examine the values 3, 6, 9, and 27 and determine which value remains under the radical when written in simplest radical form.

a) Value 3: When written in simplest radical form, the value 3 remains under the radical. Since 3 is not a perfect square, it cannot be simplified further.

b) Value 6: When written in simplest radical form, the value 6 can be simplified. The prime factorization of 6 is 2 * 3, and we can take out the perfect square factor 2. Therefore, when simplified, the value 6 becomes 2√3, with 3 remaining under the radical.

c) Value 9: When written in simplest radical form, the value 9 remains as it is. 9 is already a perfect square, and there are no other factors to simplify. Hence, 9 stays under the radical.

d) Value 27: When written in simplest radical form, the value 27 can be simplified. The prime factorization of 27 is 3 * 3 * 3, and we can take out one of the perfect square factors 3. Therefore, when simplified, the value 27 becomes 3√3, with 3 remaining under the radical.

Students solving math

When expressing numbers in their simplest radical form, the values under the radical depend on whether the number is a perfect square or has any perfect square factors. In the case of 3 and 9, which are already perfect squares, they remain under the radical. However, for values like 6 and 27, which have perfect square factors, the factors can be simplified, leaving the remaining value under the radical. It's important to understand the concept of simplest radical form and apply it when dealing with square roots or cube roots.