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Algebra I Recipe: Square Roots
A. Definitions
  1. square rooting a number – finding the number that when multiplied by itself equals the number being square rooted.


  2. perfect squares – numbers that can be square rooted evenly like 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, . . .
    • 4 = 2 because 2 • 2 = 4, BUT it could also be = -2 because –2 • -2 = 4.
    • 25 = 5 because 5 • 5 = 25, BUT it could also be = -5 because –5 • -5 = 25.
  3. means to give the positive square root or answer. 81 = 9
  4. -   means to give the negative square root or answer. -49 = -7
  5. ± means to give the positive AND negative square root or answer.  ±25 = ± 5
B. Evaluating the Expression where a = 1, b = -2, c = -3
  1. Substitute the values.
  2. Follow order of operations to find the value of the expression under the .
  3. Find the square root of the number.
    • You cannot find the square root of a negative number.
C. Evaluating an Expression like
  1. Make two problems.
    • One with only the +
    • One with only the -
  2. Use order of operations to find the two values.
    • Round the to the nearest hundredth when it cannot be square rooted evenly.
D. Pythagorean Theorem Right Triangle
  1. Pythagorean Theorem is a² + b² = c².
  2. The Pythagorean Theorem is used to find any missing side of a right triangle, when the other two lengths are known. It is also used to determine if three particular lengths would form a right triangle.
  3. "a" and "b" are the legs that form the right angle.
  4. "c" is the hypotenuse.
ExamplesExamples:
Find the missing value in the triangle shown below.


Find the missing value in the triangle shown below.





G Redden

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