Cracking The SAT Premium

2. = . For example, = = .


3. = positive root only. For example, = 4.

Note that rule 1 works in reverse: = = 5 . This is really a kind of factoring. You are

using rule 1 to factor a large, clumsy radical into numbers that are easier to work with. Rule 2 works in

reverse as well. divided by looks ugly, but = = 5. And remember that radicals are

just fractional exponents, so the same rules of distribution apply.

Careless Errors

Don’t make careless mistakes. Remember that the square root of a number between 0 and 1 is larger than

the original number. For example, = , and > .

Roots   and Your    Calculator

Another important   key is  the root    key.    On  a   scientific  calculator  it  is  often   the same    button  as  yx, but

you’ll  have    to  hit shift   first.  The symbol  is   .  So  “the    4th root    of  81” would   be  “81     4   =.”

Sometimes   the calculator  will    have    yx  or      as  xy  or   .  They    mean    the same    thing.  Just    know

which   number  you’re  supposed    to  type    in  first.

The root    key in  the TI-80   graphing    calculator  series  varies, but the most    common  symbol  is  the

square  root    sign,   which   you can get to  by  pressing    “[SHIFT]    x^2 .”  In  case    you want    to  find    the 3rd,

4th,    or  other   root    of  a   number, there   is  a   button  in  the [MATH]  directory   for     or   .  In  the case    of

the  ,  you have    to  type    in  the root    you want,   then    hit [MATH]  and  ,  and finally hit your    base

number. For example,    if  you wanted  to  find    the 4th root    of  81, you’d   type    “4  [MATH],”    then    select  

,   then    type    81  and press   [ENTER].    If  you look    at  it  on  the screen, it  will    appear  as  “4      81,”

which   is  similar to  how you’d   write   it. You can also    use the ^   symbol  if  you remember    that    a   root    is

the same    as  the bottom  part    of  a   fractional  exponent.   So  the fourth  root    of  81  would   be  written as

“81 ^   (1/4)”  on  your    calculator.

Negative and Fractional Exponents

So far we’ve dealt with only positive integers for exponents, but they can be negative integers as well as
fractions. The same concepts and rules apply, but the numbers just look a little weirder. Keep these
concepts in mind:

• Negative exponents are a fancy way of writing reciprocals: