Simplifying Radical Expressions

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Simplifying Radical Expressions

• Algebra 1

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Square Root of a Number
If b 2 a, then b is a square root of a.
Meaning Positive Square Root Negative Square Root The positive and negative square roots
Symbol
Example
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Simplifying Radical Expressions
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Simplifying Radical Expressions

• A radical has been simplified when its radicand
  contains no perfect square factors.
• Test to see if it can be divided by 4, then 9,
  then 25, then 49, etc.
• Sometimes factoring the radicand using the tree
  is helpful.

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Steps

1. Try to divide the radicand into a perfect square
   for numbers
2. If there is an exponent make it even by using
   rules of exponents
3. Separate the factors to its own square root
4. Simplify

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Simplify
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Simplify
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Simplify
Square root of a variable to an even power the
variable to one-half the power.
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Simplify
Square root of a variable to an even power the
variable to one-half the power.
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Simplify
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Simplify
 
 
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Simplify
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Simplify
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Terminology

• square root one of two equal factors of a given
  number. The radicand is like the area of a
  square and the simplified answer is the length of
  the side of the squares.
• Principal square root the positive square root
  of a number the principal square root of 9 is 3.
• negative square root the negative square root
  of 9 is 3 and is shown like
• radical the symbol which is read the
  square root of a is called a radical.
• radicand the number or expression inside a
  radical symbol --- 3 is the radicand.
  
• perfect square a number that is the square of
  an integer. 1, 4, 9, 16, 25, 36, etc are
  perfect squares.
• irrational number a number whose decimal form
  is nonterminating and nonrepeating.
• Rational number a number that can be written in
  the form a/b, where a and b are integers (b
  cannot equal 0)
• radical expression an expression that contains
  a radical.

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Simplify