# practice a simplifying radical expressions math 78

```Name
Date
Class
Practice A
LESSON
Complete the steps to simplify each expression.
2
4 8
3. 5 12 25 144 169 13
32 ___
1.
2
2. 72 8 2
6. x 2 6x 9 x
Simplify. All variables represent nonnegative numbers.
7. 72 36 2
8. 300 100 3
36 2
100 6
2
10. 500 5 100
11. 90 13.
3
4
x
__
17.
2
x
x _____
100x
___9
32
21b 2
21
b
_____ __________
4
25c 4
15.
25c
b 21
_______
4x 2
3
4x
_____
18.
2
x
__
4 2
____
1219x
5c 2
10b
_____
16b
2
5
20.
bc
2
98xy
2
10b
______
4
9
5
2
b c 2
7y 2x
2
y
19.
12.
3y
_____
10
y
9y
9y
____
______
4
16x
16x 4
1
_____
16.
10 3
2
14.
3 10
1
1 _____
____
100
100
9. b 2 c 2 b 2 c 2
3
3
9 10
10 5
8
b 4 2 b 4 4.
9
5. 10 2 19 64 _____
21.
2
11x x
________
3
3
28825x
_____
4
12x 2x
_________
5
22. A ladder is propped up against a house. The top of the ladder
rests 18 ft above the ground and the base of the ladder is 4 ft
from the building. Write the length of the ladder as a radical
expression in simplest form. Then estimate the length to the
nearest hundredth of a foot.
FT
2 85 ft; 18.44 ft
FT
Copyright &copy; by Holt, Rinehart and Winston.
a107c11-6_pr.indd 43
43
Holt Algebra 1
12/26/05 8:23:54 AM
Process Black
*&Agrave;&gt;V&Igrave;Vi&Ecirc;
--&quot;
*&Agrave;&gt;V&Igrave;Vi&Ecirc;
--&quot;
#OMPLETE THE STEPS TO SIMPLIFY EACH EXPRESSION
^
???
^
q p { &Oacute;
^
^
^
q p &Oacute;x &pound;{{ p &pound;&Egrave; &pound;&Icirc;
^
q 3IMPLIFY EACH EXPRESSION
^
q 
p^
&Egrave;{ ^
q S B D ^
X qX ^
&Egrave;
^
^
^
q ^
q q
^
q q
X
qX
Y
^
X rX &Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
^
???
&Uacute;X&Uacute;&Ecirc;
q
^
&Ecirc;&Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;{&Ecirc;r&Ecirc;&Oacute;&Ecirc;&Ecirc;
q
&Oacute;
^
&pound;&pound;&Ecirc;X &Ecirc; &Ecirc;&Ecirc;rX &Ecirc;&Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Icirc;
X&Ecirc;&Ecirc;{&Ecirc; &Ecirc;
q C
q
^
q
^
X ?????
^
n&Ecirc;&Ecirc;r &Oacute;&Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
Y&Ecirc; &Ecirc;
&Uacute;&Uacute;&Uacute;
&Ecirc;&Ecirc;&Ecirc;
^
{
N ^
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;&Oacute;M r&Oacute;&Ecirc;M &Ecirc;&Ecirc;
^
x
&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc; &Oacute;&Ecirc;{&Ecirc;&Ecirc;
&Ecirc;X &Ecirc; &Ecirc;
Q
??????
q
Q ^
x&Ecirc;Q &Ecirc;&Icirc;&Ecirc;&Ecirc;r &Oacute;&Ecirc;&Ecirc;
4WO HIKERS LEAVE A RANGER STATION AT NOON 4OM HEADS DUE
SOUTH AT MIH AND +YLE HEADS DUE EAST AT MIH (OW FAR
EXPRESSION IN SIMPLEST FORM 4HEN ESTIMATE THE DISTANCE TO
THE NEAREST TENTH OF A MILE
x
! LADDER IS PROPPED UP AGAINST A HOUSE 4HE TOP OF THE LADDER
RESTS FT ABOVE THE GROUND AND THE BASE OF THE LADDER IS FT
FROM THE BUILDING 7RITE THE LENGTH OF THE LADDER AS A RADICAL
EXPRESSION IN SIMPLEST FORM 4HEN ESTIMATE THE LENGTH TO THE
NEAREST HUNDREDTH OF A FOOT
M ?????
q
&Ecirc;N &Ecirc; &Ecirc;
????
qX
&Ecirc; &Ecirc;
&Ecirc;&Ecirc;
&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc; &Oacute;X &Ecirc;
&Ecirc;
&Ecirc;&pound;&Oacute;&Ecirc;X &Ecirc; &Ecirc;&Ecirc;r
&Oacute;
^
q????
^
M rM&Ecirc; &Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Oacute;
&Oacute;
^
^
^
Y ^
^
M ??????
qN
&pound;&pound;&Ecirc;N &Ecirc; &Ecirc;
Y
????
q
&Ecirc;r xB &Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;&Ecirc;
&Ecirc;&Ecirc;r &pound;&auml;&Ecirc; B ^
B ?????
B ^
&Egrave;&Ecirc;X &Ecirc;&Oacute;&Ecirc;Y &Ecirc;&Oacute;&Ecirc;r
&Ecirc; Y
&Icirc;B
B ?????
^
B ?????
qB
Y
&pound;&Ecirc; &Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;
^
q B
qX
&Icirc;&Ecirc;&Ecirc;rx&Ecirc;&Ecirc;
^
^
???
x
^
&Icirc;
^
^
&Ecirc; &Ccedil;&Ecirc;
r
&Ecirc; &Ecirc;&Ecirc;&Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;
X &Ecirc;&Oacute;&Ecirc;Y r^
Y
q &Ccedil;&Ecirc;&Ecirc;r&Icirc;&Ecirc;&Ecirc;
^
Y qX
^
^
&Oacute; p^
p^
&Oacute;x&Ecirc;C &Ecirc;{&Ecirc; &Oacute;&Ecirc;&Ecirc;r&Ccedil;&Ecirc;&Ecirc;
^
&Oacute;&pound;&Ecirc;B &Ecirc; &Ecirc;
B ??????????
?????
q
^
q {
^
X ?????
X&Ecirc;&Ecirc;n
q SX D q ^
^
x
^
^
{&Ecirc;&Ecirc;r&Oacute;&Ecirc;&Ecirc;
BC
x
p
B r&Oacute;&pound;&Ecirc;&Ecirc;
x&Ecirc;C &Ecirc;&Oacute;&Ecirc;
X ?????
qX
^
^
q??? p &Oacute;x qX X x
^
???????
^
X ??
q ^
C &Ecirc;&Oacute;&Ecirc;
&Ccedil;Y r &Oacute;X {&Ecirc;X &Ecirc;&Oacute;&Ecirc;
Y
q
?????
^
&Oacute;x
q
^
XY &Icirc;Y
&pound;
&pound;&auml;
q
p
^
q^
&Uacute;&Uacute;
&Ecirc;&pound;&Ecirc;
????
^
Y Y
????
??????
^
B &Ecirc;&Oacute;&Ecirc;
^
^
?????
&Icirc;&Ecirc;r &pound;&auml;&Ecirc;&Ecirc;
^
q ?????
????
^
^
&pound;&auml;&Ecirc;&Ecirc;r x&Ecirc;&Ecirc;
^
^
q ^
qB C q B C
^
&Icirc; p^
 &pound;&auml; ^
X &Ecirc;&Icirc;&Ecirc; &Ecirc;
^
&pound;&auml;&Ecirc;r &Icirc;&Ecirc;&Ecirc;
q ^
q q p
B &Ecirc;{
^
p
^
q 3IMPLIFY !LL VARIABLES REPRESENT NONNEGATIVE NUMBERS
3IMPLIFY !LL VARIABLES REPRESENT NONNEGATIVE NUMBERS
^
^
^
^
q q q &Icirc; q q &pound;x
^
n
FT
^
^
{&Ecirc;&Ecirc;r &Icirc;{&Ecirc;&Ecirc;&AElig;&Ecirc;&Oacute;&Icirc;&deg;&Icirc;&Ecirc;
&Oacute;&Ecirc;r nx&Ecirc;&Ecirc;v&Igrave;&AElig;&Ecirc;&pound;n&deg;{{&Ecirc;v&Igrave;
FT
#OPYRIGHT &copy; BY (OLT 2INEHART AND 7INSTON
!LL RIGHTS RESERVED
&Igrave;&Ecirc;}iL&Agrave;&gt;&Ecirc;&pound;
^
q ^
q????
&Icirc;&auml;
^
q S N D ^
IS IN SIMPLEST FORM IF
3IMPLIFY !LL VARIABLES REPRESENT NONNEGATIVE NUMBERS
^
q ^
q ^
^
{&Ecirc;&Ecirc;rx&Ecirc;&Ecirc;
^
q S T qX
Y
^
???
q
^
q
^
???
&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;&Ecirc;
&Ecirc;&Icirc;&Ecirc;&Ecirc;r&Ecirc;x&Ecirc;&Ecirc;
qS
^
q
B ?????
C
&Oacute;
S
X Y
??????
X Y
^
xY r &Oacute;&Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;
&Ecirc;
&Ecirc;
&Ccedil;X
^
qN &Ecirc;N &Ecirc;&Oacute;&Ecirc;
^
q
^
^
&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;&Ecirc;
&Ecirc;x&Ecirc;&Ecirc;r&Ecirc;x&Ecirc;&Ecirc;
q
^
X ????
Y
^
3IMPLIFY
&Icirc;X r &Oacute;&Ecirc;
&Ecirc;&Ecirc;&Ecirc;
&Ecirc; &Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Oacute;
^
x&Ecirc;Y &Ecirc; &Ecirc;
qX
^
?? ????
q

&Ecirc;&Uacute;&Uacute;&Uacute;
&Ecirc;{&auml;
&Ecirc;&Ecirc;&Ecirc;
q
Copyright &copy; by Holt, Rinehart and Winston.
AK4up.indd 85
3IMPLIFY
A PRODUCT
q
5SE 0RODUCT 0ROPERTY
OF 3QUARE 2OOTS
q ???
3IMPLIFY
^
3IMPLIFY
X ???
r
^
^
qX X ????
???
q
^
q Y ^
q X
??
^
^
^
q &Oacute;
5SE 1UOTIENT 0ROPERTY OF
3QUARE 2OOTS
^
^
Y Y qX
r
^
^
????
q ???
^
q rX
^
WHERE A AND B ^
???
3IMPLIFY !LL VARIABLES REPRESENT NONNEGATIVE NUMBERS
^
X X ?????
X
qX
q ^
&Ecirc;&Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc; &Oacute;&Ecirc;&Ecirc;
&Ecirc;&Ecirc;X &Ecirc; &Ecirc;r
^
^
&Oacute;&Ecirc;rx&Ecirc;&Ecirc;
&Oacute;
4HREE CRUISE SHIPS LEFT A HARBOR AT THE SAME TIME 4HE 0RINCESS 7ILMA
TRAVELED DUE NORTH AT MIH THE 0RINCE 4HEODORE TRAVELED DUE WEST
AT MIH AND THE +ING &amp;RANK TRAVELED DUE EAST AT MIH (OW FAR IS
THE 0RINCESS 7ILMA FROM THE OTHER TWO SHIPS AFTER TWO HOURS 'IVE EACH
ANSWER TO THE NEAREST TENTH OF A MILE
^
^
0RINCE 4HEODORE\&Ecirc;{&Ecirc;&Ecirc;r&pound;&Icirc;&auml;&Ecirc;&Ecirc;]&Ecirc;z{x&deg;&Egrave;&Ecirc;&AElig;&Ecirc;+ING &amp;RANK \&Ecirc;&pound;&Oacute;&Ecirc;&Ecirc;r&pound;&Icirc;&Ecirc;&Ecirc;]&Ecirc;z{&Icirc;&deg;&Icirc;&Ecirc;
#OPYRIGHT &copy; BY (OLT 2INEHART AND 7INSTON
!LL RIGHTS RESERVED
q
^
B&Ecirc;&Ecirc;&Ecirc;
&Ecirc;&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;r
&pound;&auml;
q
1UOTIENT 0ROPERTY OF 3QUARE 2OOTS
^
^
qA ?A? ???
^
B
qB Xq^
Y
B ?????
B
G
F r^
&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;
H
THERE ARE NO SQUARE ROOTS IN THE DENOMINATOR
3IMPLIFY
q ^
H G
s
&pound;{&Ecirc;C &Ecirc; &Ecirc;
F G
????
^
q q ^
x&Ecirc;B &Ecirc; &Ecirc;&Ecirc;&Ecirc;&Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;&Uacute;
&Icirc;
^
q
^
{
^
&Ecirc;&Ecirc;
&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;x&Ecirc;r &Egrave;&Ecirc;&Ecirc;
q
^
????
THE RADICAND HAS NO PERFECT SQUARE FACTORS OTHER THAN s
WHERE A AND B q q ^
{
^
????
^
^
x
^
^
A qB q AB q^
^
3IMPLIFY r
&Ccedil;X r&Oacute;Y &Ecirc; &Oacute;&pound;&Ecirc;
&Ecirc;
r
&Ecirc; &Ecirc;
&Ecirc;&Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;
q
s
0RODUCT 0ROPERTY OF 3QUARE 2OOTS
^
X Y &Ccedil;&Ecirc;XY &Ecirc;&Oacute;&Ecirc;
&pound;x&Ecirc;&Ecirc;r&Oacute;&Ecirc;&Ecirc;
ST r^
S
^
&Egrave;&Ecirc;&Ecirc;r&Icirc;&Ecirc;&Ecirc;
^
4HE EXPRESSION UNDER THE
q X N&Ecirc;&Ecirc;&pound;&auml;&Ecirc; &Ecirc;
&pound;&pound;
^
q &Igrave;&Ecirc;}iL&Agrave;&gt;&Ecirc;&pound;
,i&Igrave;i&gt;V
--&quot;
*&Agrave;&gt;V&Igrave;Vi&Ecirc;
--&quot;
3IMPLIFY EACH EXPRESSION
#OPYRIGHT &copy; BY (OLT 2INEHART AND 7INSTON
!LL RIGHTS RESERVED
&Igrave;&Ecirc;}iL&Agrave;&gt;&Ecirc;&pound;
^
???
q
^
&Ecirc; &Ccedil;&Ecirc;
r
&Ecirc; &Ecirc;&Ecirc;&Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;

#OPYRIGHT &copy; BY (OLT 2INEHART AND 7INSTON
!LL RIGHTS RESERVED
85
^
&Icirc;&Ecirc;X &Ecirc;&Oacute;&Ecirc;r
&Ecirc; &Egrave;&Ecirc;&Ecirc;
&pound;&auml;&Ecirc;r&Icirc;&Ecirc;&Ecirc;
^
^
???
q
^
&Ecirc; &pound;&auml;&Ecirc;
&Ecirc;&Ecirc;&Ecirc;
r
&Ecirc; &Ecirc;
&Ecirc;&Uacute;&Uacute;&Uacute;&Uacute;
&Icirc;
q
X ????
Y
{
&Uacute;&Uacute;&Uacute;&Uacute;
&Ecirc;&Icirc;&Ecirc;X &Ecirc;&Icirc;&Ecirc;&Ecirc;&Ecirc;
x&Ecirc;Y &Ecirc; &Ecirc;
&Igrave;&Ecirc;}iL&Agrave;&gt;&Ecirc;&pound;
Holt Algebra 1
12/26/05 8:00:58 AM
```