Objective Students will add, subtract, multiply, divide, and simplify radicals.
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Transcript of Objective Students will add, subtract, multiply, divide, and simplify radicals.
Objective
Students will add, subtract, multiply, divide, and simplify radicals.
Warm-up
• Define what a perfect square is using your own words.
• List all of the perfect squares that you can remember off the top of your head.
Simplifying Radicals
• Simplifying radicals is like creating factor trees, but we are looking for perfect square factors.
• Example:
€
8 Are there any perfect squares that are factors of 8? What are they?
€
€
4
€
2
€
€
2 2
x
Let’s try these together:
€
A. 63
€
B. 24
€
C. 306
€
D. 1024
Answers to Simplifying Radicals - Question A
€
€
A. 3 7
Answers to Simplifying Radicals Question B
€
24
€ €
€
6€
€
4€
€
2 6
Answers to Simplifying Radicals Question C
€
€
306
€
€
9€
€
34
€
3 34
3+0+6 = 9, 306 is divisible by 9 too!
Answers to Simplifying Radicals Question D
€
1024
32
€
16
€
64
€
4 • 8
Adding and Subtracting with Radicals
• Adding and subtracting with radicals is a lot like combining like terms. You can only add or subtract “like” radicals.
• Example: €
€
3 2 + 4 2 + 5 3
“Like” radicals: Add the coefficients!
€
7 2 + 5 3 Final answer!
Try these on your own!
€ €
A. 3 2 − 5 2 − 3 2 + 2
€
B. 3 − 2 3 + 4 5 − 3 5€
€
C. 20 + 5 5 + 5 2
Question A Add/Subtract
€
A. 3 2 − 5 2 − 3 2 + 2
Since each term contains radical 2, just
combine the coefficients!
€ €
€
−4 2
Question B Add/Subtract
€
B. 3 − 2 3 + 4 5 − 3 5
“like” radicals
“like” radicals
€
€
− 3 + 5
Question C Add/Subtract
€
C. 20 + 5 5 + 5 2
€
€
2 5 + 5 5 + 5 2 Simplify radicals that you can simplify.
€
€
7 5 + 5 2 Combine “like” radicals.
Multiplying with Radicals• When multiplying a radical by a
radical:– multiply the coefficients– multiply the radicals– then simplify the radical if possible.
• Example: €
€
4 5 3 2( )
€
4( ) 3( ) 5( ) 2( )
€
12 10 Final Answer?
What property?
Try these :
€ €
A. 4 3 2 12( )
€ €
B. 5 25 3 100( )
€
€
C. 3 2( ) 4 − 2 3( )
€
€
D. 5 2( )2
Question A Multiplication
€
A. 4 3 2 12( )
€
8 36
8 • 6
48
Multiply
Simplify
Final Answer
Question B Multiplication
€
B. 5 25 3 100( )
€
B. 5 25 3 100( )
Method 1 Method 2
€
5• 3• 25 • 100
15 • 2500
15 • 50
750
€
5 • 5 3• 10( )
25 30( )
750
Question C Multiplication
€
C. 3 2( ) 4 − 2 3( )
€
€
3 2 • 4( ) − 3 2 • 2 3( )
12 2 − 6 6
Distributive PropertyMultiply and Simplify
Question D Multiplication
€
D. 5 2( )2
Which answer did you choose?
€
€
Choice A - 25 4
€
€
Choice B - 25 2
€
Choice C - 50€
€
5 2( ) 5 2( )
25 4
25 2( ) = 50
Dividing with Radicals
€
€
64
16=
64
16= 4 = 2
64
16=
8
4= 2
€
€
50
10=
25 2
5 2=
25
5=
25
5= 5
50
10=
50
10= 5
Let’s kick it up a notch…Simplify using radicals.
€ €
A. 50
5
€ €
B. 63
54
€
€
C. 32
36
€
€
D. 5 + 50
5
Question A - Division
€
A. 50
5
€
€
25 5
5€
€
5 5
5
€
€
5
Simplify the radical.Take the square roots of perfect squares.
Divide by 5. This is your final answer!
Question B - Division
€
B. 63
54
Choice #1 = 1.08
Choice #2 = €
€
7
6
Choice #3 = €
€
3 7
3 6
Question C - Division
€
C. 32
36
€
16 2
6 €
€
4 2
6
€
€
2 2
3
Simplify each radical.
Take square roots.
Simplify as a fraction (if possible).
Question D - Division
€
D. 5 + 50
5
€
€
5 + 25 2
5€
€
5 + 5 2
5
€
€
5
5+
5 2
5
€
€
1+ 2