Let's break down the question step by step to find which choice is equivalent to the expression:
[tex]\[
\sqrt{50} - \sqrt{2}
\][/tex]
1. Calculate [tex]\(\sqrt{50}\)[/tex]:
- [tex]\(\sqrt{50} \approx 7.0710678118654755\)[/tex]
2. Calculate [tex]\(\sqrt{2}\)[/tex]:
- [tex]\(\sqrt{2} \approx 1.4142135623730951\)[/tex]
3. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(\sqrt{50}\)[/tex]:
- [tex]\(7.0710678118654755 - 1.4142135623730951 = 5.656854249492381\)[/tex]
So, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to approximately [tex]\(5.656854249492381\)[/tex].
Next, we need to determine which of the given choices is equivalent to this value.
- Choice A: [tex]\(4 \sqrt{2}\)[/tex]
- Calculate [tex]\(4 \sqrt{2}\)[/tex]:
- [tex]\(4 \times 1.4142135623730951 \approx 5.656854249492381\)[/tex]
- This matches our result exactly.
- Choice B: [tex]\(\sqrt{48}\)[/tex]
- Calculate [tex]\(\sqrt{48}\)[/tex]:
- [tex]\(\sqrt{48} \approx 6.928203230275509\)[/tex]
- This does not match our result.
- Choice C: [tex]\(5\)[/tex]
- This is exactly [tex]\(5\)[/tex], which does not match our result [tex]\(5.656854249492381\)[/tex].
- Choice D: [tex]\(24 \sqrt{2}\)[/tex]
- Calculate [tex]\(24 \sqrt{2}\)[/tex]:
- [tex]\(24 \times 1.4142135623730951 \approx 33.94112549695428\)[/tex]
- This does not match our result.
The correct answer is:
A. [tex]\(4 \sqrt{2}\)[/tex]
