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Mastering Radicals: Simplify and Understand Perfect Squares

Learn how to simplify radical expressions, identify perfect squares, and transform square roots into simplified forms with this comprehensive guide. Practice variable manipulations and improve your understanding of radicals.

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Mastering Radicals: Simplify and Understand Perfect Squares

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  1. Math 025 Section 10.1Radicals

  2. Square root Square root Perfect square Perfect square 1 81 Ö1 = 1 Ö81 = 9 4 100 Ö4 = 2 Ö100 = 10 9 121 Ö9 = 3 Ö121 = 11 16 144 Ö16 = 4 Ö144 = 12 25 169 Ö25 = 5 Ö169 = 13 36 196 Ö36 = 6 Ö196 = 14 49 225 Ö49 = 7 Ö225 = 15 64 Ö64 = 8

  3. Simplified radical form No factor inside the radical should be a perfect square. Ö18 = Ö2 = 3 Ö2 Ö9 Ö108 = Ö3 = 6 Ö3 Ö36 3Ö96 = Ö6 = 12 Ö6 3Ö16

  4. Simplifying variable radical expressions A variable with an even exponent is a perfect square Öx6 = x3 Öx15 = Öx = x7 Öx Öx14 4 Öx9 = 4 Öx = 4x4 Öx Öx8

  5. Simplifying radical expressions Simplify each of the following Ö16x7 = Öx 4x3 = Öx Ö16x6 5xÖx3y4 = Öx = 5x2y2 Öx 5x Öx2y4 Ö96x5y7 = Ö6xy = 4x2y3 Ö6xy Ö16x4y6

  6. Simplifying radical expressions Simplify each of the following Ö81(x – 2)2 9(x – 2) = 9x – 18 = Ö x2 + 6x + 9 ( ) = = x + 3 Ö(x + 3)2

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