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7.4 – roots of real numbers. real vs. imaginary roots – opposite of exponents!

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7.4 – Roots of Real Numbers

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Page 1: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

7.4 – Roots of Real Numbers

Page 2: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

Page 3: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Page 4: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Ex. 1 Use a calculator to approximate each value to three decimal places.

a.

b.

c.

d.

8 253.

08547.

9 8753 .25 944 .

Page 5: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Ex. 1 Use a calculator to approximate each value to three decimal places.

a. = 0.924

b. =

c. =

d. =

8 253.

08547.

9 8753 .25 944 .

Page 6: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Ex. 1 Use a calculator to approximate each value to three decimal places.

a. = 0.924

b. = no sol.

c. =

d. =

8 253.

08547.

9 8753 .25 944 .

Page 7: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Ex. 1 Use a calculator to approximate each value to three decimal places.

a. = 0.924

b. = no sol.

c. = 2.15

d. =

8 253.

08547.

9 8753 .25 944 .

Page 8: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

• Real vs. Imaginary

• Roots – opposite of exponents!

Ex. 1 Use a calculator to approximate each value to three decimal places.

a. = 0.924

b. = no sol.

c. = 2.15

d. = 2.26

8 253.

08547.

9 8753 .25 944 .

Page 9: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. =

b. =

c. 8 =

d. 2 6 =

e. 10 =

25

2435

x4

16xy

(5 )g

Page 10: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. =

c. 8 =

d. 2 6 =

e. 10 =

25

2435

x4

16xy

(5 )g

Page 11: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. = -3

c. 8 =

d. 2 6 =

e. 10 =

25

2435

x4

16xy

(5 )g

Page 12: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. = -3

c. 8 = x2

d. 2 6 =

e. 10 =

25

2435

x4

16xy

(5 )g

Page 13: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. = -3

c. 8 = x2

d. 2 6 = 4xy3

e. 10 =

25

2435

x4

16xy

(5 )g

Page 14: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. = -3

c. 8 = x2

d. 2 6 = 4xy3

e. 10 = (5g)5

25

2435

x4

16xy

(5 )g

Page 15: 7.4 – Roots of Real Numbers. Real vs. Imaginary Roots – opposite of exponents!

Ex. 2 Simplify.a. = ±5

b. = -3

c. 8 = x2

d. 2 6 = 4xy3

e. 10 = (5g)5 = 3125g5

25

2435

x4

16xy

(5 )g


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