notes day 2 book sections 7.2 and 7.3. practice radical operations 1. 2. 3
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Notes Day 2 Book sections 7.2 and 7.3
Multiply and Divide Radical Expressions
Practice Radical Operations1. 2. 3.
5459
5253
55
122122
121221224
12416
34416
3816
4
1
2
1
x
x
4
1
2
1
x
4
1
x
4 x
Practice Radical Operations4. 5.
.
23635
706
246
646
612
Simplify and rationalize all denominatorsAssume all variables are positive
6. 7.
5
3 34 yx
5
5
5
15 34 yx
5
1524 yyx
5
152 yyx
37
37
37
217321
4
21210
2
215
More rationalizing the denominator
8. 9. 10.
3 22
3
x3
3
24
xy
x4
32
1
x3
3
4
4
x
x
3 3
3
8
43
x
x
x
x
2
43 3
3 22
3 22
9
9
yx
yx
Hint: Multiply by a form of one which will eliminate the radical in the denominator!
3 33
3 23
27
216
yx
yx
xy
yx
3
6 3 2
y
y3 22
4
4
8
8
x
x
4
4
416
8
x
x
x
x
2
84
11. Find the radius of a cone that has a volume of 11 cubic inches and a height equal to its radius.
rr 2
3
111
333 r
3 3
3
3 33r
333r
3
3 33
r
3 2
3 2
3 3
3 233
r
3 233
r
12. An object moves at a speed of feet/sec. How long will it take for the object to travel 15 feet?
trd
r
dt
35
15
t
Now multiply by conjugate form of 1 to rationalize the denominator
35
35
325
31575
t .sec22
31575
13. Jim has 1 piece of wood that is 1” x ½” x 240”. He plans to cut the 240” into three pieces in the ratio of 3:4:5 to make a right
triangle. How long is the hypotenuse?
3x 4x 5x
24012 x240543 xxx
20xNow sub 20 in for each x
Dimensions are 60, 80 and 100 but…
The hypotenuse is 100”
14. A rectangular prism has dimensions 5 x 12 x 10 . What is the length of the segment that connects the front left bottom corner to the
back upper?5
10
12
222 hwld
222 10512 d
unitsd 269
49142 xx
1. Simplify 2. Find x 3. If 12 is opposite the 60° angle of a 30-60-90 triangle, find the other sides
4. Rationalize the denom.
5. Simplify.
6. Simplify. 7. Find the diagonal of a cube with a side length 2
8. Simplify 9. Rationalize the denom.
10. Rationalize the denom
xww
w
4
12
62
3
Extra Practice on HW 7.2: Work this out in your math notebook. Assume all variables are positive.
5032 53
2
272272
3 42324 zyx3 2
5
49142 xx
1. Simplify 2. Find x 3. If 12 is opposite the 60° angle of a 30-60-90 triangle, find the other sides
4. Rationalize the denom.
5. Simplify.
xww
w
4
12
62
3
Extra Practice on HW 7.2: Work this out in your math notebook. Assume all variables are positive.
7x
272272
8x3834 and 4
6 23
6. Simplify. 7. Find the diagonal of a cube with a side length 2
8. Simplify 9. Rationalize the denom.
10. Rationalize the denom
Extra Practice on HW 7.2: Work this out in your math notebook. Assume all variables are positive.
5032 53
2
3 42324 zyx
3 2
5
6. Simplify. 7. Find the diagonal of a cube with a side length 2
8. Simplify 9. Rationalize the denom.
10. Rationalize the denom
Extra Practice on HW 7.2: Work this out in your math notebook. Assume all variables are positive.
5032 53
2
3 42324 zyx3 2
5
29 323 232 zyxz
53
2
45 3