wikiHow Simplifying Radical Expressions Calculator To simplify a radical expression, you need to find the factors of the radicand (the number inside the radical symbol) that are perfect squares. You can then take the square root of those factors and bring them outside the radical symbol. Here is an example: Simplify √48 First, write 48 as a product of its prime factors: 48 = 2 * 2 * 2 * 2 * 3 Identify the factors that are perfect squares. In this case, we have four factors of 2, which is equivalent to 2^2. Rewrite the radicand using the perfect square factor(s) and simplify: √48 = √(2^2 * 2 * 2 * 3) = √(2^2) * √(2 * 2 * 3) = 2 * √(2 * 2 * 3) = 2√12 The simplified form is 2√12. Another example: Simplify √75 Write 75 as a product of its prime factors: 75 = 3 * 5 * 5 Identify the factors that are perfect squares. In this case, there are no factors that are perfect squares. Rewrite the radicand as the product of two factors, one of which is the largest perfect square that is a factor of the radicand: √75 = √(3 * 5 * 5) = √(3 * 5^2) = √(3 * 25) = √(3 * 5^2) = 5√3 The simplified form is 5√3. Page