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Simplifying radical expressions is a process of eliminating radicals or reducing the expressions consisting of square roots, cube roots, or in general, nth root to simplest form. Let us consider a few examples for simplifying radical expressions step-wise.
A radical is considered to be in simplest form when the radicand has no square number factor. Examples. Simplify the following radicals. 1. root(24) Factor 24 so that one factor is a square number. root(24)=root(4*6)=root(4)*root(6)=2root(6) 2. root(72) Find the largest square factor you can before simplifying.
Simplifying a radical is writing it in the simplest form possible so that: The index is the smallest possible. No factor of the radicand has an exponent greater than or equal to the index, so that no factor can be extracted. The radicand does not have fractions.
Express the odd powers as even numbers plus 1 then apply the square root to simplify further. Learn the basics of simplifying square root expressions with the help of examples. Find out how to recognize perfect square numbers and break down radical expressions.
Example 3: Simplify $ \sqrt{18} $ Solution: Step 1: We need to find the largest perfect square that divides into 18. Such number is 9. Step 2: Write 18 as the product of 2 and 9. ( 18 = 9 * 2 ) Step 3: Use the product rule: $ \sqrt{18} = \sqrt{\color{red}{9} \cdot \color{blue}{2}} = \sqrt{\color{red}{9}} \cdot \sqrt{\color{blue}{2}} = 3\sqrt{2} $
This calculator simplifies expressions involving radicals. The calculator reduces the radical expressions to their simplest form, trying to remove all the radicals from the expression. The calculator shows each step with easy-to-understand explanations.
"Roots" (or "radicals") are the "opposite" operation of applying exponents; we can "undo" a power with a radical, and we can "undo" a radical with a power. For instance, if we square 2 , we get 4 , and if we "take the square root of 4 ", we get 2 ; if we square 3 , we get 9 , and if we "take the square root of 9 ", we get 3 .
