Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.
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Transcript of Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.
![Page 1: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/1.jpg)
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
![Page 2: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/2.jpg)
Questions over HW?
![Page 3: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/3.jpg)
NTH ROOTS &
RATIONAL EXPONEN
TS
![Page 4: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/4.jpg)
Parts of a radical
No number where the root is means it’s a square root (2)
root radicand
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Simplifying Radicals
Break down the radicand in to prime factors.
Bring out groups by the number of the root.
root radicand
![Page 6: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/6.jpg)
Simplify
31. 128 3 2 2 2 2 2 2 2
34 2
![Page 7: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/7.jpg)
Simplify
x3 32. 27x x x 3 3 3 3
x3
![Page 8: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/8.jpg)
Simplify
x4 73. 324 2 2 2 2 2 x x x x x x x
x x 4 32 2
![Page 9: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/9.jpg)
Simplify
x934.
27x
3
3
![Page 10: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/10.jpg)
REWRITING A RADICAL TO
HAVE A RATIONAL EXPONENT
![Page 11: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/11.jpg)
Rewriting Radicals to Rational Exponents
Power is on top
Roots are in the ground
powerpower
root rootradicand radicand
![Page 12: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/12.jpg)
Rewrite with a Rational Exponent
w5. 10 w1210
![Page 13: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/13.jpg)
Rewrite with a Rational Exponent
p36. 7 p137
![Page 14: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/14.jpg)
Rewrite with a Rational Exponent
5
7. 17 5217
![Page 15: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/15.jpg)
Rewrite with a Rational Exponent
y288. y28
y14
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Rewrite with a Rational Exponent
z3 69. z63
z 2
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Rewriting Rational Exponents to Radicals
power power
rootrootradicand radicand
![Page 18: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/18.jpg)
Rewrite with a Rational Exponent
(don’t evaluate)
3510. 12
35 12
![Page 19: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/19.jpg)
Rewrite with a Rational Exponent
(don’t evaluate)
2311. 13
23 13
![Page 20: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/20.jpg)
Rewrite with a Rational Exponent
(don’t evaluate)
x3212. x
3
![Page 21: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/21.jpg)
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
![Page 22: Warm up Simplify 1. i 57 2. i 56 3. (3 + i)(4 – 2i) 4. 5. Find the exact Volume.](https://reader036.fdocuments.us/reader036/viewer/2022070413/5697bf941a28abf838c90395/html5/thumbnails/22.jpg)
SIMPLIFY
3513. 32 3
5 32
8
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SIMPLIFY2314. 64
23 64
16
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SIMPLIFY1315. 125 3 125
5
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SIMPLIFY
3416. 81
3
4181
127
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SIMPLIFY
1417. 16 4
116
12
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18. The cube below has a volume of 343 cubic inches. Find the length of an edge of the cube.
x 3343
x7
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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