RAD 1-2

RAD 1-2

1. Definitions

   • Radical
     • consists of a root symbol, an index and a radicand. it can be a rational or an irrational number
   • rationalize
     • a procedure for converting to a rational number without changing he value of the expression
   • conjugates
     • two binomial factors whose product is the difference of two squares.
   • Radicand
     • the quantity under the radical sign
   • index
     • indicates which root to take

2. Exponent laws

   • Power of a power
     • multiply the exponents keep the base the same
   • power of a product
     • multiply the exponents, keep the base the same
   • power of a quotient
     • multiply the exponents and keep the base the same
   • same base multiplication
     • if bases are the same and you are multiplying, add the exponent and keep the base the same
   • same base division
     • if the bases are the same and we divide, subtract the exponents and keep the base the same
   • zero exponent law
     • any base to the zero exponent equals 1 or -1
   • negative exponent law
     • an excess of bases in the denominator flip and drop the negative

3. key ideas/ things to know

   • how to identitfy parts of a radical
   • changing from radical form to power form
   • know how to use you calculator to evaluate radicals
   • know as many perfect square and perfect cubes as possible
   • know exponent laws
   • changing from mixed to entire is very important
   • restrictions
     • odd index: no restrictions
     • even index: radicand ≥0
   • know how to add, subtract, multiply and divide radicals
     • adding and subtracting need like terms
     • multiplication and division need to be operated on with the same type ie. rad x rad /num c x num c
   • rationalizing the denominator
     • when a radical is in the denominator both the numerator and the denominator must be multiplied by a quantity that will produce a rational denomiantor

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