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Radical Notation and Rational Exponents

  Square Root

• Not part of a tree

A number c is the square root of a if,

Careful: We only have a
positive and negative root
if there is an equation with
an equal sign
Why is 3 the square root of 9?
Why is -3 the square root of 9?
nth root

A number c is the nth root of a if,
 
Prison escape method of finding roots
Properties of Radicals

If n is even

If n is odd

Rational Exponents

 


 

The imaginary #
 
Take the exponent on i
divide by 4
the remainder is your new exponent
 
Taking roots with the TI-84

Square roots

Method 1 – hit [ ], enter the number, close the paren, hit [enter]
Method 2 – put in the number, hit [^], open a paren, type ½,
close the paren, hit [enter]

Remember, this works because the index on the radical
can be written as a rational (fractional) exponent
Cube roots

Method 1 – hit [ Math], [4], enter the number, close the paren, hit [enter]
Method 2 – put in the number, hit [^], open a paren, type 1/3
close the paren, hit [enter]
Remember, this works because the index on the radical
can be written as a rational (fractional) exponent
nth roots

Method 1 – type the index first, hit [ Math], [5], enter the number,
hit [enter]

Method 2 – put in the number, hit [^], open a paren, type 1/n
close the paren, hit [enter]

Remember, this works because the index on the radical
can be written as a rational (fractional) exponent
EXACT Answers

You must be able to use the calculator for HW and decimal approximations are fine there

You must also be able to give me EXACT Answers for tests