Answer :
To solve the problem of finding which choice is equivalent to the expression [tex]\(\sqrt{18} - \sqrt{2}\)[/tex], let's break it down step-by-step.
1. Understand the Expression:
- We need to simplify or calculate the value of [tex]\(\sqrt{18} - \sqrt{2}\)[/tex].
2. Calculate Square Roots:
- [tex]\(\sqrt{18}\)[/tex] is approximately 4.2426.
- [tex]\(\sqrt{2}\)[/tex] is approximately 1.4142.
3. Subtract the Square Roots:
- [tex]\(\sqrt{18} - \sqrt{2} = 4.2426 - 1.4142 = 2.8284\)[/tex].
Now that we have the approximate value of the expression as 2.8284, let's compare it to the given choices:
- Choice A: [tex]\(\sqrt{16}\)[/tex]
- [tex]\(\sqrt{16} = 4\)[/tex], which is not equivalent to 2.8284.
- Choice B: 3
- 3 is not equivalent to 2.8284.
- Choice C: [tex]\(2 \sqrt{2}\)[/tex]
- [tex]\(2 \times \sqrt{2} = 2 \times 1.4142 = 2.8284\)[/tex], which matches exactly with the expression's value.
- Choice D: [tex]\(16 \sqrt{2}\)[/tex]
- [tex]\(16 \times \sqrt{2} = 16 \times 1.4142 = 22.6272\)[/tex], which is much larger than 2.8284.
Based on our calculations:
- The correct and equivalent choice is Choice C: [tex]\(2 \sqrt{2}\)[/tex].
1. Understand the Expression:
- We need to simplify or calculate the value of [tex]\(\sqrt{18} - \sqrt{2}\)[/tex].
2. Calculate Square Roots:
- [tex]\(\sqrt{18}\)[/tex] is approximately 4.2426.
- [tex]\(\sqrt{2}\)[/tex] is approximately 1.4142.
3. Subtract the Square Roots:
- [tex]\(\sqrt{18} - \sqrt{2} = 4.2426 - 1.4142 = 2.8284\)[/tex].
Now that we have the approximate value of the expression as 2.8284, let's compare it to the given choices:
- Choice A: [tex]\(\sqrt{16}\)[/tex]
- [tex]\(\sqrt{16} = 4\)[/tex], which is not equivalent to 2.8284.
- Choice B: 3
- 3 is not equivalent to 2.8284.
- Choice C: [tex]\(2 \sqrt{2}\)[/tex]
- [tex]\(2 \times \sqrt{2} = 2 \times 1.4142 = 2.8284\)[/tex], which matches exactly with the expression's value.
- Choice D: [tex]\(16 \sqrt{2}\)[/tex]
- [tex]\(16 \times \sqrt{2} = 16 \times 1.4142 = 22.6272\)[/tex], which is much larger than 2.8284.
Based on our calculations:
- The correct and equivalent choice is Choice C: [tex]\(2 \sqrt{2}\)[/tex].