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08A-W3208 1/20/05 2:05 PM Page 562
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Chapter 8 Roots and Radicals
Check Your Knowledge
1.
2.
3.
4.
The principal square root of a positive real number is a
The symbol 1 is called a
4 13 is the
The
a right triangle.
number.
symbol.
of 4 13.
theorem is a formula that relates the lengths of the sides of
Simplify each radical, if possible. Assume all variables represent positive numbers.
5. 164
7.
20
B9
9. 218y4
11.
40x3
B 5y2
6. 116
3
8. 1
8
10. 228x3y4
3
16x5y6z3
12. 2
13. Evaluate 2a2 b2 for a 3 and b 4.
14. A square measures 2 feet on each side. Express the length of the diagonal of the
square in simplified radical form. Then approximate its length to the nearest
tenth.
Perform each operation.
15. 3 118 150
17. 121322 15 182
19. 12 13 2 2
16. x127x 248x3
18. 121 13 18 2
20. 1 1x 22 1 1x 22
21. The playing area of a college football field is 300 feet long and 160 feet wide.
Find the length of a diagonal of the playing field.
Rationalize each denominator.
22.
13
15x
23.
2
2 12
Solve each equation.
24. 1x 4
25. 1x 5 2 1
26. 12x 3 1x 2 0
3
27. 5 1
x72
28. Find the distance between the points (2, 5) and (3, 7).
29. Simplify: 272/3.
1
30. Simplify: 1x2 2 3/2.