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Rewrite the radicand as a product using perfect cube factors. The denominator cannot be simplified, so use the Quotient Property to write as one radical. Why didn’t we write b^2 as |b^2|? Because when you square a number, you will always get a positive result, so the principal square root of \left(b^2\right)^2 will always be non-negative.\( \newcommand\) Square roots are most often written using a radical sign, like this, \sqrt Analysis of the Solution Factor the number into its prime factors. 1) Factor the radicand (the numbers/variables inside the square root). This rule states that the product of two or more non-zero numbers raised to a power is equal to the product of each number raised to the same power. Simplifying Radical Expressions with Variables.

Recall the Product Raised to a Power Rule from when you studied exponents. Multiplying Radicals Multiply: Use the FOIL method.

• Simplify each radical expression. Example 1: Simplifying a Radical Expression with an Odd Exponent Bring the coefficient and variable together.

  Use the product rule to rewrite the radical as the product of two radicals. Rewrite the radicand as a product of two factors, using that factor. Find the largest factor in the radicand that is a perfect power of the index. Simplify radical expressions using rational exponents and the laws of exponents Simplify a radical expression using the Product Property.Simplify radical expressions using factoring.

  

  Radical expressions come in many forms, from simple and familiar, such as 16 16, to quite complicated, as in 3250x4y. Radical expressions are expressions that contain radicals.

  

  Define x2 x x 2 x and apply it when simplifying radical expressions. (9.2.4) – Rational exponents whose numerator is not equal to one Simplify radical expressions using rational exponents and the laws of exponents.If found, they can be simplified by applying the product and. (9.2.3) – Convert expressions with rational exponents to their radical equivalent To simplify radical expressions, look for factors of the radicand with powers that match the index.(9.2.2) – Convert radicals to expressions with rational exponents.Step 2 : If you have square root (), you have to take one term out of the square root for every two same terms multiplied inside the radical. Simplifying Radical Expressions Example 1: Find the square root of 144x2 144 x 2. Step 1 : Decompose the number inside the radical into prime factors. However, since the index of the radical is 3, you want the factors to be powers of 3 if possible. The following steps will be useful to simplify any radical expressions. Then, its just a matter of simplifying In this tutorial, youll see how to multiply two radicals together and then simplify their product. Solution: Start by factoring the radicands coefficient in other words, write it as a product of smaller numbers. To multiply radicals, you can use the product property of square roots to multiply the contents of each radical together. (9.2.1) – Define and identify a radical expression Example 1: Simplify the radical expressions.