Simplifying Radicals: Square Root of 12

In the world of mathematics, radicals often appear in various equations and expressions. Understanding how to simplify them is crucial for solving problems efficiently. One common radical encountered is the square root of 12. This blog post will guide you through the process of simplifying this radical, breaking it down into easy-to-follow steps.

Understanding Radicals

A radical, represented by the symbol √, signifies the root of a number. For example, √12 represents the square root of 12, which is the number that, when multiplied by itself, equals 12.

Simplifying the Square Root of 12

To simplify the square root of 12, we need to find the largest perfect square that divides 12. In this case, the largest perfect square that divides 12 is 4 (2 x 2 = 4).

Now, we can rewrite the square root of 12 as follows:

√12 = √(4 x 3)

Using the property of radicals that √(a x b) = √a x √b, we can separate the radical:

√(4 x 3) = √4 x √3

Since the square root of 4 is 2, we have:

√4 x √3 = 2√3

Therefore, the simplified form of the square root of 12 is 2√3.

Key Points to Remember

• A perfect square is a number that can be obtained by squaring an integer (e.g., 4, 9, 16).
• When simplifying radicals, always look for the largest perfect square that divides the radicand (the number under the radical sign).
• Remember the property of radicals: √(a x b) = √a x √b.

Practice Problems

Try simplifying the following radicals using the steps outlined above:

1. √20
2. √48
3. √75

By practicing these steps, you'll gain confidence in simplifying radicals and become proficient in solving various mathematical problems involving them.

Let me know if you have any further questions or need clarification on any of the concepts covered in this blog post. Happy learning!