Find nth roots

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EXAMPLE 1
Find nth roots
Find the indicated real nth root(s) of a.
a. n 3, a 216
b. n 4, a 81
SOLUTION
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EXAMPLE 2
Evaluate expressions with rational exponents
Evaluate (a) 163/2 and (b) 323/5.
SOLUTION
Rational Exponent Form
Radical Form
a. 163/2
163/2
b. 323/5
323/5
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EXAMPLE 3
Approximate roots with a calculator
a. 91/5
1.551845574
b. 123/8
2.539176951
4.303517071
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for Examples 1, 2 and 3
GUIDED PRACTICE
Find the indicated real nth root(s) of a.
1. n 4, a 625
3. n 3, a 64.
SOLUTION
5
4
SOLUTION
2. n 6, a 64
4. n 5, a 243
SOLUTION
2
3
SOLUTION
6
for Examples 1, 2 and 3
GUIDED PRACTICE
Evaluate expressions without using a calculator.
5. 45/2
7. 813/4
27
SOLUTION
32
SOLUTION
6. 91/2
8. 17/8
SOLUTION
SOLUTION
1
7
for Examples 1, 2 and 3
GUIDED PRACTICE
Evaluate the expression using a calculator. Round
the result to two decimal places when appropriate.
9. 42/5
1.74
SOLUTION
SOLUTION
0.06
SOLUTION
32
9.65
SOLUTION
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EXAMPLE 4
Solve equations using nth roots
Solve the equation.
Divide each side by 4.
Take fifth root of each side.
Simplify.
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EXAMPLE 4
Solve equations using nth roots
Take fourth roots of each side.
Add 3 to each side.
Write solutions separately.
Use a calculator.
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EXAMPLE 5
Use nth roots in problem solving
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EXAMPLE 5
Use nth roots in problem solving
SOLUTION
Write model for weight.
Substitute 200 for w.
Divide each side by 0.0167.
Take cube root of each side.
Use a calculator.
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for Examples 4 and 5
GUIDED PRACTICE
Solve the equation. Round the result to two
decimal places when appropriate.
13. x3 64
SOLUTION
SOLUTION
SOLUTION
SOLUTION
SOLUTION
SOLUTION
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for Examples 4 and 5
GUIDED PRACTICE
a. 275 grams
SOLUTION
25 cm
b. 340 grams
SOLUTION
27 cm
c. 450 grams
SOLUTION
30 cm