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Notes Day 2 Book sections 7.2 and 7.3 Multiply and Divide Radical Expressions

Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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Page 1: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

Notes Day 2 Book sections 7.2 and 7.3

Multiply and Divide Radical Expressions

Page 2: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 3: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

Practice Radical Operations4. 5.

.

23635

706

246

646

612

Page 4: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 5: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 6: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 7: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 8: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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”

Page 9: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 10: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3
Page 11: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 12: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 13: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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

Page 14: Notes Day 2 Book sections 7.2 and 7.3. Practice Radical Operations 1. 2. 3

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