Answer :
Sure! Let's simplify the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] step-by-step to find its equivalent:
1. Break down the square root of 18:
- The number 18 can be expressed as [tex]\(9 \times 2\)[/tex].
- So, [tex]\(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}\)[/tex].
2. Simplify [tex]\(\sqrt{9}\)[/tex]:
- Since [tex]\(\sqrt{9} = 3\)[/tex], we can rewrite [tex]\(\sqrt{18}\)[/tex] as:
- [tex]\(\sqrt{18} = 3 \times \sqrt{2}\)[/tex].
3. Simplify the entire expression:
- The expression now is [tex]\(3\sqrt{2} - \sqrt{2}\)[/tex].
4. Factor out [tex]\(\sqrt{2}\)[/tex]:
- You can factor out [tex]\(\sqrt{2}\)[/tex] from [tex]\(3\sqrt{2} - \sqrt{2}\)[/tex]:
- [tex]\((3 - 1)\sqrt{2} = 2\sqrt{2}\)[/tex].
So the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
The correct choice from the given options is:
D. [tex]\(2\sqrt{2}\)[/tex]
1. Break down the square root of 18:
- The number 18 can be expressed as [tex]\(9 \times 2\)[/tex].
- So, [tex]\(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}\)[/tex].
2. Simplify [tex]\(\sqrt{9}\)[/tex]:
- Since [tex]\(\sqrt{9} = 3\)[/tex], we can rewrite [tex]\(\sqrt{18}\)[/tex] as:
- [tex]\(\sqrt{18} = 3 \times \sqrt{2}\)[/tex].
3. Simplify the entire expression:
- The expression now is [tex]\(3\sqrt{2} - \sqrt{2}\)[/tex].
4. Factor out [tex]\(\sqrt{2}\)[/tex]:
- You can factor out [tex]\(\sqrt{2}\)[/tex] from [tex]\(3\sqrt{2} - \sqrt{2}\)[/tex]:
- [tex]\((3 - 1)\sqrt{2} = 2\sqrt{2}\)[/tex].
So the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
The correct choice from the given options is:
D. [tex]\(2\sqrt{2}\)[/tex]