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Warm up
Simplify1. i 57 2. i 56
3. (3 + i)(4 – 2i)4. 2
4 3
ii
i
1
i 14 2
i 1 25 5
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
Get in to your groups please.
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Worksheet