Answer :
To determine which choice is equivalent to the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], we need to simplify the expression. Let's go through the steps:
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- The number 50 can be written as [tex]\(25 \times 2\)[/tex].
- This allows us to use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex].
- Thus, [tex]\(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}\)[/tex].
2. Simplify the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
- We have now [tex]\(\sqrt{50} = 5 \times \sqrt{2}\)[/tex].
- So the expression becomes [tex]\(5 \times \sqrt{2} - \sqrt{2}\)[/tex].
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
- Both terms in the expression have a common factor of [tex]\(\sqrt{2}\)[/tex].
- Factor it out: [tex]\(5 \times \sqrt{2} - \sqrt{2} = (5 - 1) \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
The expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4 \times \sqrt{2}\)[/tex].
Therefore, the equivalent choice for the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is C. [tex]\(4 \sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- The number 50 can be written as [tex]\(25 \times 2\)[/tex].
- This allows us to use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex].
- Thus, [tex]\(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}\)[/tex].
2. Simplify the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
- We have now [tex]\(\sqrt{50} = 5 \times \sqrt{2}\)[/tex].
- So the expression becomes [tex]\(5 \times \sqrt{2} - \sqrt{2}\)[/tex].
3. Factor out [tex]\(\sqrt{2}\)[/tex]:
- Both terms in the expression have a common factor of [tex]\(\sqrt{2}\)[/tex].
- Factor it out: [tex]\(5 \times \sqrt{2} - \sqrt{2} = (5 - 1) \times \sqrt{2} = 4 \times \sqrt{2}\)[/tex].
The expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4 \times \sqrt{2}\)[/tex].
Therefore, the equivalent choice for the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is C. [tex]\(4 \sqrt{2}\)[/tex].