PreCalculus Class Notes RP3 Operations with Radicals
Operations with Radicals
Multiply/Divide Radicals
( 3x
5 x3
)( 4 15x )
2
3
8m 3 n 4
⋅
n
m2
3 4 64 x 7
4
2x
Multiply/Divide Radicals with Different Indices
3
3
a 3b2 ⋅ a 2b
Add/Subtract Radicals (Like Terms)
2 4 64 − 4 324 + 4 4
3 xy 2 − x
16 ⋅ 4 8
3
xy 4 + 3 x 4 y
Distribute and Combine Radicals
(
(5 − 5 )(5 + 3 5 )
x −2 3
)
2
Rationalize Radicals (Monomial Denominator)
1
8
5b
72
3 5x
2 2x
Rationalize Radicals (Binomial Denominators)
3 −1
2 z
3+2
2− z