unit 2a: simplifying radicals and imaginary/complex numbers€¦ · unit goals students will be...
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Unit Goals
▪ Students will be able to:
▪ Simplify Radicals of varying index
▪ Add, Subtract, Multiply, and Divide Radicals
▪ Rationalize the denominator when presented with
radicals and radical expressions
▪ Identify and simplify complex and imaginary numbers
Reducing Radicals
▪ Method 1: Perfect Factors
1. “Break down” (a.k.a. factor) the number
inside the radical, using the largest “perfect”
factor.
2. Rewrite the radical as a product of two factors.
3. Cross out the perfect root and write what it
equals in front of the radical.
4. Bring down any “left-overs,” and write them
with a multiplication sign between them.
5. Multiply the numbers in front of the radical.
Reducing Radicals
▪ Method 2: Groups
1. “Break down” (a.k.a. factor) the number
inside the radical. Write out the prime
factorization
2. Determine the group amount.
3. Circle all groups (if any).
4. Write one number from each group outside of
the radical. Multiply these numbers.
5. Leave any “left-over” numbers inside the
radical and multiply.
Properties of Radicals
▪ Product Property
▪ 𝑎 × 𝑏 = 𝑎𝑏
▪ Just multiply the numbers underneath the radical!
▪ Simplify radicals either before OR after multiplying.
▪ If there are numbers out front, multiply them first.
▪ Quotient Property
▪𝑎
𝑏=
𝑎
𝑏
▪ A fraction underneath a radical can be broken up into a
fraction of radicals.
▪ We cannot have radicals left in the denominator. To
rationalize the denominator, multiply the numerator and
denominator by the radical in the denominator (for
square roots only)
Adding and Subtracting
Radicals
▪ To add and subtract radicals, treat the radicals like
variables!
▪ We can only combine like terms.
▪ The type of radical AND the number inside the radical
MUST be the same in order to add/subtract.
▪ It is possible that we cannot add or subtract radicals.
▪ You cannot add or subtract two radicals with different
indexes.
Adding and Subtracting Examples
1. 3 + 3
2. 5 + 8 5
3. 6 7 − 8 7
4. 2 + 3
5. 237 + 2
37
6. 348 −
48
7. 635 + 8 5
8. 5316 + 7
354
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