6.3 Notes Fisher
Algebra 2
6.3 Notes
Name:
Date: MARCH
Pd: 9
6.3 – Binomial Radical Expressions
WARM-UP
Try This!!!
Simplify.
3𝑟 − 2𝑎 + 3𝑟 2 + 5𝑟 − 10𝑑 + 14𝑎
I. Adding and Subtracting Radicals
To simplify the previous expression, you may only combine LIKE terms.
Similarly, there must be LIKE RADICALS to combine radicals.
Like Radicals:_____________________________________________________________ √2
radicand
Examples of:
Like Radicals:
√2
√2
Unlike radicals:
√5
√2 √3
TEACHER DO
Examples
Simplify.
1. 3√2 + 5√2
√2
Step 1: Take out what they have in common; take out like radical
(3 + 5) √2 Step 2: Add the coefficients
8√2
2. √8 + √98
√8= √4 + √2
√98= √49 + √2
= 2 √2 + 7 √2
= (2+7) √2
= 9 √2
1
6.3 Notes Fisher
3
3
3. √81 − √24
3
3
3
(√33 · √3) = √81 Step 1: Factor & Reduce/Simplify (27·3 = 81)
3
3
3
( √2³ · √3) = √24
(8·3) = 24
3
3
3√3 - 2 √3 =
Step 2: Take out like radical
3
(3-2) √3 =
Step 3: Subtract the Coefficients
3
√3
3
4. 2√5 + 3√5
Can Not Add- Index is Different, therefore already simplified
3
3
5. √27 − √8
3
3
√3³ − 1√8
3
(3-1) √8
3
2√8
STUDENTS DO
7. √27 + √12 − √75
8. √245 + 3√125
10. 3 3√3𝑥𝑦 + 3√24𝑥𝑦
11. √48 + √162
4
4
3
3
3
9. √250 − √54 + √4
12. √81𝑥 + √64𝑥
2
6.3 Notes Fisher
TEACHER DO
II. Distributing.
We can also distribute with radicals.
1. Multiply Using FOIL, First, Outer, Inner, Last
2. Combine Like Terms
8. √6(√2 + √3)
√6 ·√2 = √12
+
√6 · √3 = √18
9. (2+√3) (3√2- √5)
FOIL
2·3√2 - 2√5 + √3 ·3√2 - √5·√3
6√2 - 2√5 + 3√6 -√15
= √12 + √18
10. (3 + √5)²
(3 + √5) (3 + √5)
= 9+ 3 + √5 +3 + √5 + 5 First Step: Foil
=(9+5) + (3+3)√5
Second Step: Combine like Terms
= 14 + 6√5
3
6.3 Notes Fisher
STUDENTS DO
III. Multiplying Binomials Containing Radicals.

1. 5 
3.


3 3  2 3 FOIL
6  116  11 FOIL
6. (√3 − √5)(2√3 − 5√5) FOIL
2
2. ( 7  11) FOIL



4. 7  2 5 7  2 5 FOIL
7. (2 − 2√3)(2 − 2√3) FOIL
4
6.3 Notes Fisher
TEACHER NOTES
Conjugates: Are binomial
expressions that differ only in the sign of the second term.
Example: √3 + √2 and √3 - √2
rational number
*The product of Conjugates is always an
(√2 + √3 ) (√2 + √3 )
2-√6 + √6 -3 = -1


What is the conjugate of 2  3 ?
√2 - √3


of 2 5  4 3 ?
2√5 + 4√3
The idea of conjugates can be valuable when we need to rationalize a denominator.
IV. Rationalizing a denominator with a binomial.
TEACHER DO
6.
6
3-√5
18- 6√5
18- 6√5
3 + √5
3-√5
3²- (√5)²
9-5
·
=
=
=
18- 6√5
4
=
9-3√5
2
STUDENTS DO
2 + √3
7.
1 - √3
Step #1: FOIL
Step #2: Combine Like Terms
5