Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Match the radical to its simplified form.

a. [tex]\sqrt{-50}[/tex]
b. [tex]\sqrt{-252}[/tex]
c. [tex]4 \sqrt{54}[/tex]
d. [tex]\sqrt{-81}[/tex]

1. [tex]5 i \sqrt{2}[/tex]
2. [tex]12 \sqrt{6}[/tex]
3. [tex]9 i[/tex]
4. [tex]6 i \sqrt{7}[/tex]

Sagot :

GinnyAnswer
Let's match each of the given radicals to their simplified forms step-by-step.

### Step-by-Step Solution:

#### Matching a: [tex]\(\sqrt{-50}\)[/tex]

1. To simplify [tex]\(\sqrt{-50}\)[/tex]:
- Introduce the imaginary unit: [tex]\( \sqrt{-50} = \sqrt{50} \cdot \sqrt{-1} = \sqrt{50} \cdot i \)[/tex].
- Simplify [tex]\(\sqrt{50}\)[/tex]: [tex]\( \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5 \sqrt{2} \)[/tex].
- Therefore, [tex]\(\sqrt{-50} = 5 i \sqrt{2}\)[/tex].

#### Matching b: [tex]\(\sqrt{-252}\)[/tex]

2. To simplify [tex]\(\sqrt{-252}\)[/tex]:
- Introduce the imaginary unit: [tex]\( \sqrt{-252} = \sqrt{252} \cdot \sqrt{-1} = \sqrt{252} \cdot i \)[/tex].
- Simplify [tex]\(\sqrt{252}\)[/tex]: [tex]\( \sqrt{252} = \sqrt{36 \cdot 7} = \sqrt{36} \cdot \sqrt{7} = 6 \sqrt{7} \)[/tex].
- Therefore, [tex]\(\sqrt{-252} = 6 i \sqrt{7}\)[/tex].

#### Matching c: [tex]\(4 \sqrt{54}\)[/tex]

3. To simplify [tex]\(4 \sqrt{54}\)[/tex]:
- Simplify [tex]\(\sqrt{54}\)[/tex]: [tex]\( \sqrt{54} = \sqrt{9 \cdot 6} = \sqrt{9} \cdot \sqrt{6} = 3 \sqrt{6} \)[/tex].
- Therefore, [tex]\(4 \sqrt{54} = 4 \cdot 3 \sqrt{6} = 12 \sqrt{6}\)[/tex].

#### Matching d: [tex]\(\sqrt{-81}\)[/tex]

4. To simplify [tex]\(\sqrt{-81}\)[/tex]:
- Introduce the imaginary unit: [tex]\( \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = \sqrt{81} \cdot i \)[/tex].
- Simplify [tex]\(\sqrt{81}\)[/tex]: [tex]\( \sqrt{81} = 9 \)[/tex].
- Therefore, [tex]\(\sqrt{-81} = 9 i\)[/tex].

### Final Matches:

a. [tex]\(\sqrt{-50}\)[/tex] matches with [tex]\(5 i \sqrt{2}\)[/tex] (option 1).

b. [tex]\(\sqrt{-252}\)[/tex] matches with [tex]\(6 i \sqrt{7}\)[/tex] (option 4).

c. [tex]\(4 \sqrt{54}\)[/tex] matches with [tex]\(12 \sqrt{6}\)[/tex] (option 2).

d. [tex]\(\sqrt{-81}\)[/tex] matches with [tex]\(9 i\)[/tex] (option 3).

Thus, the correct matches are summarized as follows:
- a. [tex]\(\sqrt{-50}\)[/tex] = 5 i [tex]\(\sqrt{2}\)[/tex] (option 1)
- b. [tex]\(\sqrt{-252}\)[/tex] = 6 i [tex]\(\sqrt{7}\)[/tex] (option 4)
- c. [tex]\(4 \sqrt{54}\)[/tex] = 12 [tex]\(\sqrt{6}\)[/tex] (option 2)
- d. [tex]\(\sqrt{-81}\)[/tex] = 9 i (option 3)

The matches are: [tex]\( (1, 4, 2, 3) \)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.