This is a free lesson from our course in Algebra II
In this section you'll learn the concepts from how to add and subtractsquare roots or radicals. Adding and subtracting radicals
is similar to adding and subtracting polynomial terms. If radicals are same, we
can apply basics for adding like terms (i.e. distributive property). E.g. adding 32
+ 42,
yields
2(3
+ 4) = 72
and subtracting 65
- 25,
gives
5(6
- 2) = 45.If the radicals are not same, the sum or difference of unlike radicals cannot always
be expressed as a single term. In some cases, you can explore to transform unlike
radicals into equivalent like radicals. For example, subtracting (575
-
300),
yields 153.
One of the major misconceptions in square root arithmetic is that you can add the radicands to combine square roots with addition, but this is not true.
If a and b are two positive real numbers, then in general: a + b (a +b)
The same can be said about subtraction of square roots.
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2
+ 4