Radicals

Radicals

1. Simplifying Radicals

   • Radical expressions are simply square roots, cube roots, etc.
     • • In order to simplify radicals, one must know their perfect squares because radicals are the inverse of perfect squares.
       • How to simplify radicals: First of all, one must find all the factors of the given radicand. One must choose the pair of factors that are the largest PERFECT SQUARE. Next, rewrite the radical as a product of the square root. Lastly, simplify the radical.
         • • 16 and 5 are both factors of 80. 16 is a perfect square. So, as you see they are shown as the factors of 80. Then, the square root of 16 is 4, so it is underneath 16. Since 5 is a prime number it stays as square root of 5.

2. Adding and Subtracting Radicals

   • Each radicand must be the same in order for one to be able to simplify the expression. If the radicands are like terms, all you do is add the numbers outside of the radical. The radicand remains the same. However, if the coefficients are not the same, you must simplify the radicand until it is a prime number using the factor tree.

3. Multiplying Radicals

   • First, make sure the index is the same. Second, multiply the radicands. Finally, simplify the radical expression to its simplest form.

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