How to Simplify Non Perfect Square Roots
Non perfect square roots can be quite challenging to simplify, especially for those who are just beginning to learn about square roots. However, with a few simple steps and a bit of practice, you can easily simplify these square roots. In this article, we will discuss the methods and techniques to simplify non perfect square roots.
Firstly, it’s important to understand that a non perfect square root is a square root that cannot be simplified further by removing any perfect square factors. For example, the square root of 12 is a non perfect square root because it cannot be simplified further by removing any perfect square factors.
To simplify a non perfect square root, you can follow these steps:
1. Prime factorize the number under the square root.
2. Group the prime factors into pairs.
3. Take the square root of each pair and multiply the results together.
Let’s take the square root of 12 as an example:
1. Prime factorize 12: 12 = 2 × 2 × 3
2. Group the prime factors into pairs: (2 × 2) × 3
3. Take the square root of each pair and multiply the results together: √(2 × 2) × √3 = 2√3
As you can see, the square root of 12 can be simplified to 2√3.
Another method to simplify non perfect square roots is by using the conjugate. The conjugate of a binomial expression is formed by changing the sign between the terms. For example, the conjugate of (a + b) is (a – b).
To simplify a non perfect square root using the conjugate, follow these steps:
1. Multiply the original expression by its conjugate.
2. Simplify the resulting expression by rationalizing the denominator.
Let’s take the square root of 3 + 2√2 as an example:
1. Multiply the original expression by its conjugate: (3 + 2√2)(3 – 2√2)
2. Simplify the resulting expression: 3^2 – (2√2)^2 = 9 – 8 = 1
The square root of 3 + 2√2 can be simplified to 1.
In conclusion, simplifying non perfect square roots can be done by prime factorizing the number under the square root, grouping the prime factors into pairs, and taking the square root of each pair. Alternatively, you can use the conjugate method to simplify binomial expressions involving square roots. With practice and patience, you’ll be able to simplify non perfect square roots with ease.
