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**Radical Functions & Rational Exponents**

Unit Objectives: Simplify radical and rational exponent expressions Solve radical equations Find the inverse of a function: algebraically & graphically Identify function attributes: domain and range Perform function operations: add, subtract, multiply & compose Todayβs Objective: I can simplify radical expressions.

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**Review of Exponent Properties**

π π β
π π = π π+π (π π ) π = π πβ
π (ππ) π = π π β
π π π 0 = 1 π π π π = π 1 π π π π π = π π π π πβπ π βπ = Simplify with positive exponents only. 3 π₯ β2 π¦ 3 π₯ 5 π¦ 7 β1 2 π₯ 5 β
3 π₯ 8 (3 π₯ 5 π¦ β3 ) 2 9 π₯ 10 π¦ 6 6 π₯ 13 π₯ 7 π¦ 4 3

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**Roots & Radical Expressions**

Powers Roots Radicals 2 2 = 4 2 is the square root of 4 4 = 2 2 = 2 2 3 = 8 2 is the cube root of 8 3 8 = = 2 2 4 = 16 2 is the fourth root of 16 4 16 = = 2 π π = π a is the nth root of b π π = π π π = π Index: Degree of root Radicand

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**Simplifying Radicals π π π = π, if π is odd π , if π is even 3 π₯ 12 =**

Write radicand in factors raised to the nth power or less. Take the nth root of all factors to the nth power. Simplify in front of radical and under radical. 3 π₯ 12 = 3 π₯ 3 β
π₯ 3 β
π₯ 3 β
π₯ 3 25 = 5 2 = 5 3 125 = = =π₯β
π₯β
π₯β
π₯ = π₯ 4 5 3 β27 = 3 (β3) 3 = β3 5 32 π₯ 10 = β
π₯ 5 β
π₯ 5 3 64 = 3 8β
8 =2β
π₯β
π₯ = 2π₯ 2 = β
2 3 = 2β
2= 4

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**Simplifying Radicals π π π = π, if π is odd π , if π is even**

Write radicand in factors raised to the nth power or less. Take the nth root of all factors to the nth power. Simplify in front of radical and under radical. 3 54 π₯ 5 = 3 27β
2β
π₯ 3 β
π₯ 2 24 = 4β
6 2 2 β
6 = 2 6 = β
2β
π₯ 3 β
π₯ 2 =3π₯ 3 2 π₯ 2 3 24 = 3 8β
3 4 48 π₯ 13 = 4 16β
3β
π₯ 4 β
π₯ 4 β
π₯ 4 β
π₯ β
3 = 2 3 3 = β
3β
π₯ 4 β
π₯ 4 β
π₯ 4 β
π₯ =2β
π₯β
π₯β
π₯ 4 3π₯ =2 |π₯ 3 | 4 3π₯

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