10-3 Operations With Radical Expressions
Quick Review
You can use th e properties of real n u m b ers to com bine
radical expressions. To simplify radical expressions such as
2
^ + , multiply the numerator and denominator by the
conjugate of the denominator, V 5 - 3.ExampleWhat is the simplified form of
2V5 2V5 V5-21V5 + 2 V5 + 2 V 5 - 2
2V5(V5 - 2)
_ (V5 + 2)(V5 - 2)
_ 10 - 4V5
1
= 1 0 -4 V 5M u ltip ly byV5-2
V5-2'Multiply fractions.Simplify the numerator and
denominator.
Simplify the fraction.Exercises
Simplify each radical expression.- 5V 6-3V 6
- V 2 (V 8 + V 6 )
- (3 V 2 — 2 V 5 ) (4 V 2 + 2 V 5 )
35.V2 - 3
V3 - 3
V3 + 3- Geometry A golden rectangle is 3 in. long. The
ratio of its length to its w idth is (1 + V 5 ) : 2. W hat
is the w idth of the rectangle? Write your answ er in
sim plified radical form.
10-4 Solving Radical Equations
Quick Review
You can solve som e radical equations by isolating the
radicals, squaring b o th sides of th e equation, a n d th e n
testing the solutions.
Some solutions m ay be extraneous. Some eq u atio n s m ay
have no solution.
ExampleWhat is the solution of Vx + 16 = V9x?
Vx + 16 = V9x
(V x+ 16)2 = (V9x)2
x + 16 = 9x
16 = 8x
2 = x
Check V2 + 16 ^ V9(2)
Vl8 = Vl8
The solution is 2.Square each side.
Simplify.
Subtract x from each side.
Divide each side by 8.
Substitute 2 for x.Exercises
Solve each radical equation. Check your solution. If there
is no solution, write no solution.- Vx — 5 = 8
- Vw - 2 = 4
- V2 + d = d
- nV2 = V 9 -3n
38. 4 + V y = 7 - V/+4 = 5
- 2Vr= V3r+ 1
- 2x = V 2 - 2 x
- Geometry Ihe radius r of a cylinder is given by the
equation r -- 7 rh, w here Vis th e volum e an d h is
the height. If th e radius of a cylinder is 3 cm an d the
height is 2 cm, w h at is th e volum e of th e cylinder?
R ound to th e n ea rest te n th of a cubic centim eter.
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