Adding and Subtracting Radicals
To find the sum of
and
we can use a calculator to get
and
(The symbol ≈ means â€œis approximately equal to.â€) We can then add
the decimal numbers and get
We cannot write an exact decimal form for
; the number 3.146 is an approximation
of
. To represent the exact value of
, we just use
the form
. This form cannot be simplified any further. However, a sum of
like radicals can be simplified. Like radicals are radicals that have the same index
and the same radicand.
To simplify the sum
, we can use the fact that 3x
+ 5x = 8x is
true for any value of x. Substituting
for x gives us
. So like radicals can be combined just as like terms are combined.
Example 1
Adding and subtracting like radicals
Simplify the following expressions. Assume the variables represent positive
numbers.
Solution
Only like radicals are combined.
