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Lesson 9: Rational Exponents and Radicals Digging Deeper solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 1 of 4
Radical Equations Activity
Solve.
1. 20
2 7x
x=
−
( )
( ) ( )
( ) ( )
22
2
2
20
2 7
20
2 7
400
2 7
4002 7 2 7
2 7
2 7 400
2 7 400 0
2 25 16 0
xx
xx
xx
x x xx
x x
x x
x x
=−
=
−
=−
− ⋅ = − −
− =
− − =
+ − =
2 25 0 or 16 0
25 or 16
2
x x
x x
+ = − =
= − =
25
2x ≠ − since x cannot be negative
Check: 16x =
( )
?
?
?
?
2016
2 16 7
204
25
204
5
4 4
=−
=
=
= �
Answer: 16x =
Lesson 9: Rational Exponents and Radicals Digging Deeper solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 2 of 4
2. 2 5 2 1 0z z+ + + − =
To solve this, we’ll isolate one of the radicals and square both sides.
Then we’ll isolate the other radical and square both sides again.
( ) ( )( )
( ) ( )( )
( ) ( )
2 2
22
2
2
2
2 5 2 1 0
2 5 1 2
2 5 1 2
2 5 1 2 2 2
2 2 2
2 2 2
4 4 4 2
4 4 4 8
4 0
2 2 0
z z
z z
z z
z z z
z z
z z
z z z
z z z
z
z z
+ + + − =
+ = − +
+ = − +
+ = − + + +
+ = − +
+ = − +
+ + = +
+ + = +
− =
+ − =
2 0 or 2 0
2 or 2
z z
z z
+ = − =
= − =
Check: 2z = − 2z =
( ) ( )
?
?
?
?
?
2 5 2 1 0
2 2 5 2 2 1 0
1 0 1 0
1 0 1 0
0 0
z z+ + + − =
− + + − + − =
+ − =
+ − =
= �
( ) ( )
?
?
?
?
?
2 5 2 1 0
2 2 5 2 2 1 0
9 4 1 0
3 2 1 0
4 0
z z+ + + − =
+ + + − =
+ − =
+ − =
= �
Answer: 2z = −
Lesson 9: Rational Exponents and Radicals Digging Deeper solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 3 of 4
3. ( )3
419 27 0m − − =
( )
( )
( )
( )( )
3
4
3
4
443 334
43
4
19 27 0
19 27
19 27
19 27
19 3
19 81
100
m
m
m
m
m
m
m
− − =
− =
− =
− =
− =
− =
=
Check: 100m =
( )
( )
( )
( )( )
3 ?
4
3 ?
4
3 ?
4
?34
?3
?
?
19 27 0
100 19 27 0
81 27 0
81 27 0
3 27 0
27 27 0
0 0
m − − =
− − =
− =
− =
− =
− =
= �
Answer: 100m =
Lesson 9: Rational Exponents and Radicals Digging Deeper solutions
Algebra 1
© 2009 Duke University Talent Identification Program
Page 4 of 4
4. Find the distance between the points (4, 8) and (-2, 5).
( )( ) ( )
( ) ( )
2 2
2 2
4 2 8 5
6 3
36 9
45
9 5
3 5
d = − − + −
= +
= +
=
= ⋅
=
Distance is 3 5
