Warm up
Simplify
1. i 58 2. i 106
3.(3 + i)(4 – 2i)4. 80
11
i 14 2
4 5i
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
TI – 36X ProPrime Factors for
YOU1. Type in the number
you need to prime factor
2. Press math3. Scroll down to the 4th
one Pfactor and enter
(or just press math 4)
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
x 7
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
x 4.7
Get in to your quads please.
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Worksheet
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