How to Simplify Radicals: Radicals are mathematical expressions that involve square roots, cube roots, or other roots. Simplifying radicals is an important skill that can make solving math problems easier and faster. In this article, we will provide a step-by-step guide on how to simplify radicals.

Step 1: Identify the perfect squares

The first step in simplifying a radical is to identify any perfect squares that are factors of the radicand. A perfect square is a number that is the square of an integer. For example, 4 is a perfect square because it is equal to 2 squared. Similarly, 9 is a perfect square because it is equal to 3 squared.

Step 2: Factor the radicand

Next, factor the radicand into its prime factors. For example, if the radicand is 12, you can factor it as 2 x 2 x 3.

Step 3: Simplify the radical

Now that you have factored the radicand, you can simplify the radical by taking out any perfect squares. For example, the square root of 12 can be simplified as follows:

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√12 = √(2 x 2 x 3) = 2√3

In this example, 4 is a perfect square that is a factor of 12, so we can take it out of the radical and write it as 2. The remaining factor, √3, cannot be simplified any further.

Step 4: Simplify the expression

Finally, simplify the entire expression by combining any like terms. For example, if you are asked to simplify the expression √27 + 2√12, you can use the steps above to simplify each radical:

√27 = √(3 x 3 x 3) = 3√3 2√12 = 2(2√3) = 4√3

Now you can combine the like terms:

√27 + 2√12 = 3√3 + 4√3 = 7√3

In conclusion, simplifying radicals is an important skill in mathematics that can make solving problems easier and faster. By following the steps above, you can simplify radicals and simplify expressions involving radicals. Practice simplifying radicals to become more confident in your math skills.