Answer :
To solve the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], we can simplify it step-by-step:
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- [tex]\(\sqrt{50}\)[/tex] can be expressed as [tex]\(\sqrt{25 \times 2}\)[/tex].
- This can be further broken down using the property of square roots: [tex]\(\sqrt{a \times b} = \sqrt{a} \cdot \sqrt{b}\)[/tex].
- So, [tex]\(\sqrt{50} = \sqrt{25} \cdot \sqrt{2} = 5 \cdot \sqrt{2}\)[/tex].
2. Simplify the whole expression:
- Now, we have [tex]\(5\sqrt{2} - \sqrt{2}\)[/tex].
- Both terms have [tex]\(\sqrt{2}\)[/tex], so we can combine the like terms.
- [tex]\(5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}\)[/tex].
Therefore, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex], which matches choice C.
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- [tex]\(\sqrt{50}\)[/tex] can be expressed as [tex]\(\sqrt{25 \times 2}\)[/tex].
- This can be further broken down using the property of square roots: [tex]\(\sqrt{a \times b} = \sqrt{a} \cdot \sqrt{b}\)[/tex].
- So, [tex]\(\sqrt{50} = \sqrt{25} \cdot \sqrt{2} = 5 \cdot \sqrt{2}\)[/tex].
2. Simplify the whole expression:
- Now, we have [tex]\(5\sqrt{2} - \sqrt{2}\)[/tex].
- Both terms have [tex]\(\sqrt{2}\)[/tex], so we can combine the like terms.
- [tex]\(5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}\)[/tex].
Therefore, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex], which matches choice C.