How to Simplify Radical Expressions

Step-by-Step Guide

1. 1

   Step 1: Simplify any radical expressions that are perfect squares.

   A perfect square is the product of any number that is multiplied by itself, such as 81, which is the product of 9 x
   9.
   
   To simplify a perfect square under a radical, simply remove the radical sign and write the number that is the square root of the perfect square.
   
   For example, 121 is a perfect square because 11 x 11 is
   121.
   
   Thus, you can simplify sqrt(121) to 11, removing the square root symbol.
   
   To make this process easier, you should memorize the first twelve perfect squares: 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25, 6 x 6 = 36, 7 x 7 = 49, 8 x 8 = 64, 9 x 9 = 81, 10 x 10 = 100, 11 x 11 = 121, 12 x 12 = 144
2. 2

   Step 2: Simplify any radical expressions that are perfect cubes.

   A perfect cube is the product of any number that is multiplied by itself twice, such as 27, which is the product of 3 x 3 x
   3.
   
   To simplify a radical expression when a perfect cube is under the cube root sign, simply remove the radical sign and write the number that is the cube root of the perfect cube.
   
   For example, 343 is a perfect cube because it is the product of 7 x 7 x
   7.
   
   Therefore, the cube root of the perfect cube 343 is simply
   7.

Detailed Guide

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