2,3,6,8. Are the following numbers constructible or not:

• 2. cube root of 3
• 3. 3 + 4(sqrt(7))
• 6. sqrt(2 + sqrt(3) + sqrt(5))
• 8. cube root of (5 + cube root of 7))

Solution:2) is not constructible, 3) is constructible, 6) is constructible, 8) is not constructible.

10. Take a given unit segment and two other given segments. Find a segment whose measure is the difference of the two given segments.

Solution:

11. Take a given unit segment and two other given segments. Find a segment whose measure is the product of the two given segments.

Solution:

13. Take a given unit segment and two other given segments. Find a segment whose measure is the square root of the measure of the longer segment.

Solution:

For exercises 16-19, with a given unit segment, construct segments for each of these numbers in the set of constructible numbers. Use the results of one exercise for the next.

16.3

17. sqrt(3)

18. 2 + sqrt(3)

19. sqrt(2 + sqrt(3))

Solutions: