Included are 3 topics:
1. Constructing Pythagorean Triples (4 different methods)
2. Constructing Continued Fractions from radicals
3. Using Perfect Squares to approximate radicals
All three of these have been employed historically for practical and conceptual reasons.
The PREVIEW will give you a good idea of the actual worksheet.
[The problems in All WORKSHEETS and PREVIEWS are printed in difficulty (1 [easy], 2 [not so easy], 3 [proficiency] up to 4 [mastery]) order within a skill. The actual difficulty level appears slightly to the left of the DK box of each problem in a very small font. Also, instructional references appear on worksheets but are optional on quizzes.]
You might also want to check out the Grade 8 Summary
which has links to many related offerings here.
In addition, the following are 2 other unusual units and question sets for more advanced classes: the Grade 8 (and up) UNIT: Square Root Approximations
and Grade 8 (and up) Theorems, formulas and problems for the Gifted/Curious
Further, you might also want to check out the Grades 4, 5 and 6 HISTORICAL problems