Roots and Radicals
Roots are the flip side of exponents, just as division
is the flip side of multiplication. When you square a number, you
multiply it by itself. So 5 squared is (5)(5) = 25. Square roots
go in the opposite direction. To get the square root of 25, you
need to find the number that when multiplied by itself equals 25.
The answer is 5.
The SAT is very fond of square roots, but you should know
how to work with other roots as well. The basic concept is this:
To calculate the value of
,
you have to find a number that, when multiplied by itself
b times,
gives
a:
Roots are similar to exponents in two other ways:
-
Addition/Subtraction. Can you add or
subtract exponents? Nope. The same is true for roots. You cannot
just add or subtract them. You have to work out each root separately.
Only then can you add or subtract:
-
Multiplication/Division. As with exponents,
this is allowed. If the roots are of the same degree, you can multiply
and divide two roots by simply multiplying or dividing the numbers
under the radical sign:
