1. Solve equations using nth roots
EXAMPLE 4
Solve equations using nth roots
Solve the equation.
a. 4x5
= 128 x5 32 =
Divide each side by 4. x =  32 5
Take fifth root of each side. x 2 =
Simplify.

2. Solve equations using nth roots
EXAMPLE 4
Solve equations using nth roots
b. (x – 3)4
= 21
x – 3 4 + –  21 =
Take fourth roots of each side. x  4 + – 21
+ 3 =
Add 3 to each side. x 4  21
+ 3 = or –
Write solutions separately. x
5.14 or
0.86
Use a calculator.

3. EXAMPLE 5
Use nth roots in problem solving
Biology
A study determined that the weight w (in grams) of coral cod near Palawan Island, Philippines, can be approximated using the model
w = ℓ 3
where l is the coral cod’s length (in centimeters). Estimate the length of a coral cod that weighs 200 grams.

4. Use nth roots in problem solving
EXAMPLE 5
Use nth roots in problem solving
SOLUTION w
l 3 =
Write model for weight.
200
l 3 =
Substitute 200 for w.
11,976
l 3
Divide each side by
11,976 3  l
Take cube root of each side.
22.9 l
Use a calculator.
ANSWER
A coral cod that weighs 200 grams is about 23 centimeters long.

5. GUIDED PRACTICE
for Examples 4 and 5
Solve the equation. Round the result to two decimal places when appropriate.
16. 1 4
x3 = 2
x3 = 64
SOLUTION x
= 4
SOLUTION x
= 2
14. 1 2
x5 = 512
17.
( x – 2 )3 = –14
SOLUTION x
= –0.41
SOLUTION x
= 4
15.
3x2 = 108
18.
( x + 5 )4 = 16
SOLUTION
SOLUTION x –
= + 6 x
= – 3 or
= –7

6. GUIDED PRACTICE
for Examples 4 and 5
WHAT IF? Use the information from Example 5 to estimate the length of a coral cod that has the given weight.
19.
a grams
SOLUTION
25 cm
b grams
SOLUTION
27 cm
c grams
SOLUTION
30 cm