Use properties of radicals

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Simplify Radical Expressions

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Presentation transcript:

Use properties of radicals EXAMPLE 3 Use properties of radicals Use the properties of radicals to simplify the expression. a. 12 3 18 12 18 3 = 216 3 = = 6 Product property b. 80 4 5 80 5 4 = = 16 4 = 2 Quotient property

Write radicals in simplest form EXAMPLE 4 Write radicals in simplest form Write the expression in simplest form. a. 135  3 = 27  3 5 Factor out perfect cube. = 27  3 5 Product property 5  3 = Simplify.

Write radicals in simplest form EXAMPLE 4 Write radicals in simplest form b. 7  5 8 7  5 8 4 = Make denominator a perfect fifth power. 25 = 32 35 = 243 45 = 1024 32  5 28 = Product property 28  5 2 = Simplify.

Add and subtract like radicals and roots EXAMPLE 5 Add and subtract like radicals and roots Indices must match! In this case each index is 4, so operation is allowed Simplify the expression. a. 10  4 7 + = 10  4 (1 + 7) = 10  4 8 b. (81/5) 2 + 10 = (81/5) (2 +10) = (81/5) 12 c. 54  3 – 2 = 2  3 27 – 2  3 – = 2  3 (3 – 1) = = 2  3

GUIDED PRACTICE for Examples 3, 4, and 5 Simplify the expression. 27 4 3 3 4 5 24  5 2 SOLUTION 3 SOLUTION 2  3 250 5  3 40 + SOLUTION 5 SOLUTION 3 5 

EXAMPLE 6 Simplify expressions involving variables Simplify the expression. Assume all variables are positive. a. 64y6  3 = 43(y2)3  3 43  3 (y2)3 = = 4y2 b. (27p3q12)1/3 = 271/3(p3)1/3(q12)1/3 = 3p(3 1/3)q(12 1/3) = 3pq4 = m4  4 n8  = m4 4 (n2)4 = m n2 c. m4 n8 4 d. 14xy 1/3 2x 3/4 z –6 = 7x(1 – 3/4)y1/3z –(–6) = 7x1/4y1/3z6

Write variable expressions in simplest form EXAMPLE 7 Write variable expressions in simplest form Write the expression in simplest form. Assume all variables are positive. a. 4a8b14c5  5 = 4a5a3b10b4c5  5 Factor out perfect fifth powers. a5b10c5  5 4a3b4 = Product property 4a3b4  5 ab2c = Simplify.

Write variable expressions in simplest form EXAMPLE 7 Write variable expressions in simplest form b. x y8 3 = x y8 y 3 Make denominator a perfect cube. = x y y9 3 Simplify. x y  3 y9 = Quotient property x y  3 y3 = Simplify.

EXAMPLE 8 Add and subtract expressions involving variables Perform the indicated operation. Assume all variables are positive. a. 1 5  w + 3 = 1 5 + 3  w = 4 5  w b. 3xy1/4 8xy1/4 – = (3 – 8) xy1/4 = –5xy1/4 12 c. z 2z5  3 – 54z2 = 12z 2z2  3 – 3z (12z – 3z) 2z2  3 = 9z 2z2  3 =

GUIDED PRACTICE for Examples 6, 7, and 8 Simplify the expression. Assume all variables are positive. 3x 1/2 y 1/2 6xy 3/4 27q9  3 SOLUTION 3q3 2x1/2y1/4 SOLUTION x10 y5 5 w 9w5  – w3 x2 y SOLUTION SOLUTION 2w2  w