Answer :
To solve the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex], we can start by simplifying each square root.
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
- We know that 18 can be factored into 9 and 2, where 9 is a perfect square.
- So, [tex]\(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we have [tex]\(\sqrt{18} = 3\sqrt{2}\)[/tex].
2. Simplify the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex]:
- Now substitute the simplified result for [tex]\(\sqrt{18}\)[/tex]:
- So, [tex]\(\sqrt{18} - \sqrt{2} = 3\sqrt{2} - \sqrt{2}\)[/tex].
3. Combine like terms:
- You can factor out [tex]\(\sqrt{2}\)[/tex] from both terms:
- This becomes [tex]\((3\sqrt{2} - 1\sqrt{2}) = (3 - 1)\sqrt{2} = 2\sqrt{2}\)[/tex].
Thus, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
Therefore, the correct choice is D. [tex]\(2\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{18}\)[/tex]:
- We know that 18 can be factored into 9 and 2, where 9 is a perfect square.
- So, [tex]\(\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we have [tex]\(\sqrt{18} = 3\sqrt{2}\)[/tex].
2. Simplify the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex]:
- Now substitute the simplified result for [tex]\(\sqrt{18}\)[/tex]:
- So, [tex]\(\sqrt{18} - \sqrt{2} = 3\sqrt{2} - \sqrt{2}\)[/tex].
3. Combine like terms:
- You can factor out [tex]\(\sqrt{2}\)[/tex] from both terms:
- This becomes [tex]\((3\sqrt{2} - 1\sqrt{2}) = (3 - 1)\sqrt{2} = 2\sqrt{2}\)[/tex].
Thus, the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex] simplifies to [tex]\(2\sqrt{2}\)[/tex].
Therefore, the correct choice is D. [tex]\(2\sqrt{2}\)[/tex].