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Please show work:

Evaluate, if possible
6.
 121
= sqrt(-1)sqrt(121)
= 11i
12.
4
25
= sqrt(4)/sqrt(25)
= 2/5
24.
3 
8
27
= 3 * sqrt(-1) * sqrt(4/9) * sqrt(2/3)
= 3i * sqrt(4)/sqrt(9) * sqrt(2/3)
= 3i * 2/3 * sqrt(2/3)
= 2i * sqrt(2/3)
(this is about 1.63i)
68. Science and medicine. Find the time required for an object to fall to the ground
from a building that is 1400 ft high. (Use the formula found in exercise 67.)
The formula is missing from 67: “is given by[SOMETHING] in which”
(67. Science and medicine. The time in seconds that it takes for an object to fall from
rest is given by in which s is the distance fallen. Find the time required
for an object to fall to the ground from a building that is 800 ft high.)
Use Property 1 to simplify each of the following radical expressions. Assume that all variables
represent positive real numbers.
2. 50
= sqrt(25)*sqrt(2)
= 5sqrt(2)
24.
72 x
3
=sqrt(36x^2)*sqrt(2x)
=sqrt(36)*sqrt(x^2)*sqrt(2x)
=6x*sqrt(2x)
Use Property 2 to simplify each of the following radical expressions.
10
49
36. .
= sqrt(10)/sqrt(49)
= sqrt(10)/7
Use the properties for radicals to simplify each of the following expressions. Assume that
all variables represent positive real numbers
42.
5
3
= sqrt(5)/sqrt(3)
Multiply the top and bottom by sqrt(3):
= sqrt(5)sqrt(3)/3
= sqrt(15)/3
48.
12 x
3
5
= sqrt(12x^3) / sqrt(5)
= sqrt(4x^2)*sqrt(3x) / sqrt(5)
= 2x * sqrt(3x) / sqrt(5)
Multiply the top and bottom by sqrt(5):
= 2x * sqrt(3x) * sqrt(5) / 5
= 2x * sqrt(15x) / 5
32.
63 - 2 28 + 5 7
= sqrt(9)*sqrt(7) – 2*sqrt(7)*sqrt(4) + 5*sqrt(7)
= 3sqrt(7) – 4sqrt(7) + 5sqrt(7)
= 4sqrt(7)
50. Geometry. Find the perimeter of the triangle shown in the figure.
Add the side lengths:
4 + sqrt(5) – sqrt(3) + sqrt(5) + sqrt(3)
= 4 + 2sqrt(5)


Perform the indicated multiplication. Then simplify each radical expression.
4.
13 • 5
= sqrt(13*5)
= sqrt(65)
28.
7 (2 3 +3 7 )
= 2*sqrt(3)*sqrt(7) + 3*sqrt(7)*sqrt(7)
= 2*sqrt(21) + 3*7
= 2*sqrt(21) + 21
Perform the indicated division. Rationalize the denominator if necessary. Then simplify
each radical expression.
50.
18  567
9
= [18 + sqrt(81*7)] / 9
= 18/9 + sqrt(81)*sqrt(7)/9
= 2 + 9*sqrt(7)/9
= 2 + sqrt(7)
52.
 9! 108
3
Is that really an exclamation point? I’m guessing that it’s not:
= [-9 – sqrt(36*3)] / 3
= -9/3 – sqrt(36)*sqrt(3)/3
= -3 – 6sqrt(3)/3
= -3 – 2sqrt(3)
If it was supposed to be an exclamation, let me know.
54.
6  20
2
= 6/2 – sqrt(4*5)/2
= 3 – sqrt(4)*sqrt(5)/2
= 3 – 2*sqrt(5)/2
= 3 – sqrt(5)
58. Geometry. Find the area of the rectangle shown in the figure.
Area = length * width
= (sqrt(3) + sqrt(5))(sqrt(3) + sqrt(5))
Using FOIL;
= 3 + sqrt(5)sqrt(3) + sqrt(3)sqrt(5) + 5
= 8 + 2*sqrt(5)sqrt(3)
= 8 + 2sqrt(15)
Challenge:
P.810
Evaluate root
21. 144
= sqrt(16*9)
= sqrt(16)*sqrt(9)
= 4*3
= 12