Section 10.2: Adding and Subtracting Radical Expressions Worksheet 10.2
Definition: we say that two radical expressions are like radicals if the
index and radicand are the same.
Example: $4\sqrt{2}$ and $-2\sqrt{2}$ are like radicals since they both
contain $\sqrt{2}.$
Example: $4\sqrt{3}$ and $-3\sqrt{2}$ are unlike radicals since they both
contain different radicals.
Adding/Subtracting Like Radicals
Fact: Similar to like terms involving a variable, we can add/subtract like radicals.
Example: Subtract. $$4\sqrt{2}-2\sqrt{2}$$
Notice: The above example is similar to the subtraction problem $$4x-2x.$$
Examples
$2\sqrt{13}+5\sqrt{13}$
$2\sqrt[3]{3}+6\sqrt[3]{3}-9\sqrt[3]{3}$
$5\sqrt{7 q}+4\sqrt{7 q}$
$6\sqrt{19}+9\sqrt{13}+4\sqrt{19}+5\sqrt{13}$
Simplifying Radicals Before Adding
Fact: sometimes we need to simplify radicals before we can see that they are like radicals.
Example: Simplify the radical expression $\sqrt[3]{81 h^{4}}.$
Example:: Subtratct $\sqrt[3]{704}-\sqrt[3]{88}$
Example: Subtract $5\sqrt{32 n}-3\sqrt{8 n}$
More Examples
$2\sqrt{99 \xi^2}-4\sqrt{275 \xi^2}$
$4\sqrt[5]{7 \mu}+9\sqrt[5]{7 \mu}+5\sqrt[5]{7 \mu}$