Algebra I Honors : Quarter 4 Exam Review ANSWER KEY 10-1 Pythagorean Theorem Determine if each set of lengths can be the side lengths of a right triangle. 1. 12, 60, 61 12 2 + 60 2 = 61 2 144 + 3600 = 3721 3744 ≠ 3721 No 2. 15, 36, 39 15 2 + 36 2 = 39 2 225 + 1296 = 1521 1521 = 1521 Yes 3. 12, 35, 38 12 2 + 35 2 = 38 2 144 + 1225 = 1444 1369 ≠ 1444 No 10-2 Simplifying Radicals Simplify each radical expression. (Rationalize the denominator, if applicable.) 4. 192 s 2 64 s 2 ⋅ 3 = 8 s 3 5. 3 150b 8 3 25b 8 ⋅ 6 = 3 ⋅ 5b 4 6 = 15b 4 6 6. 20 x 2 y 3 4 x 2 y 2 ⋅ 5 y = 2 xy 5 y 7. 3x 3 64 x 2 3x 64 = 3x 8 8. 2 24 48t 4 2 2 ⋅ t 4 = 2 t 2 2 = 2 2 2t 2 = 2 t 2 9. 3xy 17 507 x 5 y 9 y 8 169 x 4 = y 4 13x 2 10. 4 10 i 2 90 4 ⋅ 2 ⋅ 10 ⋅ 90 = 8 900 = 8 ⋅ 30 = 240 11. 3 5c i 7 15c 2 3 ⋅ 7 ⋅ 5 ⋅ 15 ⋅ c 3 = 21 25c 2 ⋅ 3c = 21 ⋅ 5c 23c = 105c 3c 12. −6 15n 5 i 2 75 −6 ⋅ 2 ⋅ 15 ⋅ 75 ⋅ n 5 = −12 225n 4 ⋅ 5n = −12 ⋅ 15n 2 5n = −180n 2 5n ? ? ? ? ? ?
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Algebra I Honors – Quarter 4 Exam Review...Quarter 4 Exam Review ANSWER KEY 10-1 Pythagorean Theorem Determine if each set of lengths can be the side lengths of a right triangle.
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Algebra I Honors: Quarter 4 Exam Review
ANSWER KEY 10-1 Pythagorean Theorem Determine if each set of lengths can be the side lengths of a right triangle.
1. 12, 60, 61
122 + 602 = 612
144 + 3600 = 37213744 ≠ 3721
No
2. 15, 36, 39
152 + 362 = 392
225 +1296 = 15211521= 1521
Yes
3. 12, 35, 38
122 + 352 = 382
144 +1225 = 14441369 ≠ 1444
No
10-2 Simplifying Radicals Simplify each radical expression. (Rationalize the denominator, if applicable.)
4. 192s2
64s2 ⋅3 = 8s 3
5. 3 150b8
3 25b8 ⋅6 = 3⋅5b4 6 =
15b4 6
6. 20x2y3
4x2y2 ⋅5y = 2xy 5y
7. 3x3
64x2
3x64
=3x8
8. 2 2448t 4
22 ⋅ t 4
= 2t 2 2
= 2 22t 2
=2t 2
9. 3xy17
507x5y9
y8
169x4=
y4
13x2
10. 4 10 i 2 90 4 ⋅2 ⋅ 10 ⋅90 = 8 900 = 8 ⋅30 =
240
11. 3 5c i 7 15c2
3⋅7 ⋅ 5 ⋅15 ⋅c3 =
21 25c2 ⋅3c = 21⋅5c 23c = 105c 3c
12. −6 15n5 i 2 75
−6 ⋅2 ⋅ 15 ⋅75 ⋅n5 =
−12 225n4 ⋅5n = −12 ⋅15n2 5n = −180n2 5n
? ?
? ?
?
?
13. 27
27⋅ 77=2 77
14. 58x 5
4 ⋅2x= 52 2x
⋅ 2x2x
=
10x2 ⋅2x
=10x4x
15. 3 615
3 615
⋅ 1515
= 3 9 ⋅1015
=
3⋅3 1015
=3 105
10-3 Operations with Radical Expressions Simplify each expression. (Rationalize the denominator, if applicable.)