Simplifying Radicals
Simplifying Radicals
 To simplify a radical
 1) Factor the radicand to primes
 2) “Each pair is one square”
take each pair from under the radical as one value
 3) Multiply any values in front for new coefficient
 4) Multiply any values left inside for new radicand
Simplifying Radicals
 Simplify the following radicals
54
60
Simplifying Radicals
 Simplify the following radicals
162
196
Simplifying Radicals
 Simplify the following radicals
5 44
6 72
Simplify Radicals
 Simplify the following radicals
128
8 300
Multiplying/Dividing Radicals
 Coefficients can multiply/divide and stay outside
 Radicands can multiply/divide and stay inside
 Simplify as before
 Shortcut
 Remember
3 3 3
Multiply/Divide Radicals
8 5 2 3
4 2 3 2
6 3
2 3
Multiply/Divide Radicals
18  2
6 3
2 3
3 2 5 8
Add/Subtract Radicals
 In order to add or subtract terms, the radicands must be the
same, the rules are just like those for variables, add the
coefficients and leave the radicands.
4 5 3 5  7 5
3 5  2 3 • Do not simplify
Add/Subtract Radicals
 Always remember to see if your terms will simplify before
you give up!
18  50  3 2  5 2  8 2
Add/Subtract Radicals
5 7 2 7
6 2 5 3
45  60
2 27  4 48
Rationalize a term
 To rationalize a term means to clear any radicals from the
denominator.
 To do that we multiply by a “fancy form of 1” that matches
the radical we want to remove from the bottom.
 Ex:
5
5
3 5 3
becomes


3
3
3
3
Rationalizing
 Rationalize
4
7
5 2
5
8
2
PRACTICE
 WS