Section 9 – 1:
Square Roots of Perfect Squares
Selected Worked Homework Problems
1 = 1!
4 = 2!
9 = 3!
16 = 4 !
25 = 5 !
36 = 6 !
49 = 7 !
81 = 9 !
100 = 10 !
121 = 11!
144 = 12!
169 = 13!
196 = 14 !
225 = 15
64 = 8
!
Simplify the following square roots.
1.
9
!
2.
25 !
3.
81 !
9 = 3• 3
so
!
25 = 5 • 5
so
!
81 = 9 • 9
so
9=3
25 = 5
81 = 9
25
!
16
13.
14.
25
16
Put the numerator and
denominator under
separate radical signs
36
!
169
36
169
Put the numerator and
denominator under
separate radical signs
!
25
16
simplify
5
=
4
=
Math 100 !
49
!
121
15.
49
121
Put the numerator and
denominator under
separate radical signs
!
36
169
simplify
6
=
13
=
Section 9 – 1 HW WKD !
49
121
simplify
7
=
11
=
© 2016 Eitel
2
!
98
21.
50
32
22.
!
Reduce the fraction that is
inside the radical sign
Reduce the fraction that is
inside the radical sign
2
1
=
98
49
Put the numerator and
denominator under
separate radical signs
50
25
=
32
16
Put the numerator and
denominator under
separate radical signs
!
1
49
simplify
1
=
7
25
16
simplify
5
=
4
=
29.
=
121 − 144 + 9 !
64 − 16 + 25 !
30.
first simplify
each square root
first simplify
each square root
121 − 144 + 9
!
then simplify
= 11− 12 + 3
=2
64 − 16 + 25
then simplify
= 8− 4 +5
=9
33. −2 81
32. 6 25 !
−2 81
means
6 25
means
6 times
!
25
6 • 25
= 6• 5
= 30
Math 100 !
!
−2 times
−2 • 81
= −2 • 9
= −18
Section 9 – 1 HW WKD !
81
!
© 2016 Eitel
34. 2 100 − 4 81 !
35. 3 100 − 49
first simplify
each square root
first simplify
each square root
2 100 − 4 81
2 •10 − 4 • 9
3 100 − 1 49
3•10 − 1• 7
!
then simplify
20 − 36
−16
−16
44.
25
!
64
then simplify
30 − 7
23
45. 27
means
25
64
5
= −16 •
8 !
cancel
−16 •
=
−1/ 6/ 2 5
• 1
1
8/
= −10
Math 100 !
64
!
81
!
means
64
81
8
= 27 •
9
cancel
27 •
=
27 3 8
•
1 9/ 1
= 24
Section 9 – 1 HW WKD !
© 2016 Eitel