Algebra 1 Common Core Student Edition, Grade 8-9

Have you solved
problems like this
before?
Yes. You have s u b stitu te d
a v a lu e f o r o n e v a ria b le
in a fu n c tio n and th e n
solved for the other
variable.

Think _
How can you make
the equation sim pler
to solve?
You can s o lve a s im p le r
problem by squaring
each side o f th e
e q u a tion. You k n o w h o w
to solve equations like
51-11 = f + 5.

Pr o b l em 2 Using a Rad ical Equat ion

Clocks The time 1 in seconds it takes for a pendulum of a clock to complete a full

swing is approximated by the equation 1 = 2 \/~^$> where € is the length of the

pendulum, in feet. If the pendulum of a clock completes a full swing in 3 s, what is the

length of the pendulum? Round to the nearest tenth of a foot.

• A function relating t
  and i


• The value of t

4!feisL-w

The va lu e fo r €,

the length o f the

pendulum

&L_

Substitute for t in the

function and solve for €.

1=2

3 = 2

1.5 =

(1*5) = I t2_ \/

2.25 33

7.425 = €

Check 3 = 2 7.4253.3

3 = 2V2525

3 = 3

Substitute 3 for t.

Divide each side by 2 to isolate the radical.

Square each side.

Simplify.

Multiply each side by 3.3.

Substitute 7.425 for i.

The pendulum is about 7.4 ft long.

Go t I t? 2. How long is a pendulum if each swing takes 1 s?

Solving Wit h Rad ical Ex p r essio n s on Bot h Sid es

What is the solution of V51 - 11 = Vl + 5?

V51- 11 = Vf+5

( V 5 f - l l ) 2 = ( V l+ 5 ) 2 Square each side.

5t — 11 = 1+5 Simplify.

4 1- 11 =5 S u b tra c t 1 fr o m ea ch side.

41= 16 Add 11 to each side.

1=4 Divide each side by 4.

Check V5(4) - 11 = V4 + 5 Substitute 4 for t.

V9= V9

& Got It? 3. What is the solution of V7x — 4 = V5x + 10?

634 Chapter 10 Radical Expressions and Equations