warm up simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. find the exact volume

Warm up

Simplify1. i 57 2. i 56

3. (3 + i)(4 – 2i)4.

5. Find the exact Volume

2

4 3

ii

i

1

i 14 2

i 1 25 5

2 318 18 384 cm

3

Questions over HW?

NTH ROOTS &

RATIONAL EXPONEN

TS

Parts of a radical

No number where the root is means it’s a square root (2)

root radicand

Simplifying Radicals

Break down the radicand in to prime factors.

Bring out groups by the number of the root.

root radicand

Simplify

31. 128 3 2 2 2 2 2 2 2

34 2

Simplify

x3 32. 27x x x 3 3 3 3

x3

Simplify

x4 73. 324 2 2 2 2 2 x x x x x x x

x x 4 32 2

Simplify

x934.

27x

3

3

REWRITING A RADICAL TO

HAVE A RATIONAL EXPONENT

Rewriting Radicals to Rational Exponents

Power is on top

Roots are in the ground

powerpower

root rootradicand radicand

Rewrite with a Rational Exponent

w5. 10 w1210

Rewrite with a Rational Exponent

p36. 7 p137

Rewrite with a Rational Exponent

5

7. 17 5217

Rewrite with a Rational Exponent

y288. y28

y14

Rewrite with a Rational Exponent

z3 69. z63

z 2

Rewriting Rational Exponents to Radicals

power power

rootrootradicand radicand

Rewrite with a Rational Exponent

(don’t evaluate)

3510. 12

35 12

Rewrite with a Rational Exponent

(don’t evaluate)

2311. 13

23 13

Rewrite with a Rational Exponent

(don’t evaluate)

x3212. x

3

SIMPLIFYSometimes you can simplify in the calculator.

KNOW how to do it by hand!!

Change to a radical

Prime Factor

Bring out groups

of the root

SIMPLIFY

3513. 32 3

5 32

8

SIMPLIFY2314. 64

23 64

16

SIMPLIFY1315. 125 3 125

5

SIMPLIFY

3416. 81

3

4181

127

SIMPLIFY

1417. 16 4

116

12

18. The cube below has a volume of 343 cubic inches. Find the length of an edge of the cube.

x 3343

x7

19. The volume of a basketball is approximately 448.9 cubic inches. Find the radius of the basketball to the nearest tenth.

r 34448.9

3

x4.7