Math 097 Sample Quiz #8 Key (Text Sections 7.1-7.6)
Instructions: Show all your work in the space provided and clearly indicate your final answer.
Use proper mathematical notation (such as equal signs between things that are equal!)
1. Simplify. Answers should be given in simplified radical form.
3
3
3
3
√48 = √8 ∙ 6 = √23 ∙ 6 = 2 √6
1
11
√𝑥 4
6
√𝑥 6 = |𝑥|
=
1
11
11
√𝑥 7
11
√𝑥 4 √𝑥 7
11
=
√𝑥 7
11
√𝑥 11
11
√𝑥 7
=
𝑥
5 √5 √7 √35
√ =
∙
=
7 √7 √7
7
4
54
= √ = √18 = √32 ∙ 2 = 3√2
3
√3
√54
3√10 − 2
=
4
∙
3√10 + 2
3√10 − 2 3√10 + 2
4(3√10 + 2)
=
9 ∙ 10 − 4
4(3√10 + 2)
=
86
2(3√10 + 2) 6√10 + 4
=
=
43
43
2. Perform the indicated operations and simplify. Answers should be in simplified radical form.
(5√2 − 7)(3 − 8√14 ) = 15√2 − 40√28 − 21 + 56√14
= 15√2 − 40√22 ∙ 7 − 21 + 56√14
= 15√2 − 80√7 − 21 + 56√14
7
√6
3
7
√6
+ 4√ 22 ∙ 6
√6 √6
7√6
=
+ 8√6
6
7 48
= ( + ) √6
6 6
55
=
√6
6
+ 4√24 =
7
2
∙
5
2 5
14 15
29
21
21
21
√𝑥 2 ∙ √𝑥 5 = 𝑥 3 ∙ 𝑥 7 = 𝑥 3+7 = 𝑥 21+21 = 𝑥 21 = √𝑥 29 = √𝑥 21 𝑥 8 = 𝑥 √𝑥 8
2
5
3. Write in radical form: 3𝑥 5 = 3 √𝑥 2