Section 5.5 Radicals and Roots. Def: For any real numbers a and b, if b = a 2 then a is a square root of b. So: But: Then a is a square root of b.

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Presentation transcript:

Section 5.5 Radicals and Roots

Def: For any real numbers a and b, if b = a 2 then a is a square root of b. So: But: Then a is a square root of b

1. Squaring and square root undo each other They are inverse operations 2.

PowersFactorsRoots a 3 = = 64 4 is the cube root of 64 a 4 = 16 a 5 = 243 a n = b 2222 =16 2 is the fourth root of = is the fifth root of 243 aaa….. n factors of a a is the n’th root of b

Def: For any real numbers a and b, and any positive integer n, if a n = b then a is an n th root of b a 2 = b a is the square root of b IfThen a 3 = b a 8 = b a n = b a is the cube root of b a is the 8 th root of b a is the n th root of b

3. 4. Find

Notation: Radical Radicand Index When there is more than one real root, the nonnegative root is called the principal root When no index is given It is the Principal Square root

5.) Solve x =  8 is said: ( plus (+) and minus ( - ) 8 )

6.) Find each root: 7.) Find:

8.) Find the root: The index is not shown Principal square root Because the index is even the square root could be either ± 2. So, use  absolute value To find the non-negative value or Principal Square root 9.) Find:

Approximate using a calculator (3 decimal places)

Homework Page 285 Problems: # all