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Algebra 1 Notes SOL A.3 Radicals Mrs. Grieser Name: _______________________________________ Date: _______________ Block: ________ Radical Review A perfect square is ______________________________________________. The first 12 perfect squares are:____________________________________________________. A square root of a number is ______________________________________________________. Find: Estimating square roots: find the closest perfect square 36 49 x2 144 35 o Estimate to the nearest whole number: 4x 4 55 99 Other roots: o A perfect cube is ______________________________________________. o The first 10 perfect cubes are:___________________________________________________. o A cube root of a number is _____________________________________________________. 3 Find: y means the xth root of y. The the radicand. By default, take the square root. Example: 3 8 3 27 3 x 125 x3 3 8x 6 symbol is called a radical. The number inside is 42 4= 2 Simplifying Radicals A radical expression is in simplest form if: No perfect squares other than 1 are in the radicand No fractions are in the radicand No radicals appear in the denominator of a fraction We use the Product Property of Radicals and Quotient Property of Radicals to simplify: Quotient Property of Radicals The square root of a quotient equals the quotient of the square roots of the a a numerator and denominator: ab a b b b Write the radicand as the product of perfect squares, and then take the roots of those perfect squares. a) Simplify 32 b) Simplify 9x 3 Product Property of Radicals The square root of a product equals the product of the square roots of the factors: 32 = 16 2 = 16 ∙ 2 = 4 2 9x 3 = 9 x2 x = You try: Simplify the radical expressions… a) Simplify 24 b) Simplify 25x2 9 ∙ x 2 ∙ x = 3x x Algebra 1 Notes SOL A.3 Radicals Mrs. Grieser Page 2 Examples for Quotient Property of Radicals: a) Simplify 13 = 100 13 13 = 10 100 b) Simplify 1 = y2 1 y2 = 1 y Multiplying Radicals We can use the product property of to multiply radicals. Examples: a) 6∙ 6 = 36 =6 3x ∙4 x = 4 3x x b) (makes sense!) = 4 3x = 3 7x 2 y 2 2 = 3xy 7 = 4x 3 Note: When we solve 7xy2 ∙3 x c) x 2 , we always take the positive value of x. Rationalizing Denominators The process of eliminating a radical in a denominator is called rationalizing the denominator. Examples: Rationalize the denominator… 5 7 5 5 7 7 = ∙ = 7 7 7 a) b) = 4 2x 2 2x 4 4 2x 2x ∙ = = x 2x 2x 2x You try: Simplify the radical expressions… a) 20 d) 96x2 1 x g) j) 3 27x3 b) 72 c) e) 9x 16 f) h) 2x 2 5 i) 16x4 l) k) 3 32x5 4 3 8 3n2 3 64x6 y 9 8