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Radicals Parts of a Radical • Radical Symbol: the symbol √ or indicating extraction of a root of the quantity that follows it • Radicand: the quantity under a radical sign • Index: • If there is no Index number written, then it in an understood 2! Simplifying Radicals 1. Find the prime factorization of the number inside the radical. 2. Determine the index of the radical. 3. Move each group of numbers or variables from inside the radical to outside the radical. 4. Simplify the expressions both inside and outside the radical by multiplying. Adding and Subtracting • We can add or subtract LIKE radicals. (i.e. they MUST have the SAME RADICAND when SIMPLIFIED) • Treated like combining like terms. • Simply add or subtract the coefficients and keep the radical the same! Multiplying • Product Property: Dividing • Quotient Property: Rationalize the Denominator • A quotient with a square root in the denominator is NOT simplified. • To simplify, multiply the fraction by “1” to get a perfect square radicand in the denominator. • Ex.