Answer :
To find which choice is equivalent to the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], let's simplify the expression step by step:
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The expression inside the square root can be broken down:
[tex]\[
50 = 25 \times 2
\][/tex]
Since [tex]\(25\)[/tex] is a perfect square, we can write:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\][/tex]
2. Substitute [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex]:
Our original expression becomes:
[tex]\[
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}
\][/tex]
3. Simplify the expression:
Factor out [tex]\(\sqrt{2}\)[/tex] from both terms:
[tex]\[
5\sqrt{2} - \sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Now, compare this with the given choices:
- A. 5 is just a number and not equivalent to [tex]\(4\sqrt{2}\)[/tex].
- B. [tex]\(4\sqrt{2}\)[/tex] matches exactly with the simplified expression.
- C. [tex]\(\sqrt{48}\)[/tex] simplifies to:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\][/tex]
This is different from [tex]\(4\sqrt{2}\)[/tex].
- D. [tex]\(24\sqrt{2}\)[/tex] is much larger than [tex]\(4\sqrt{2}\)[/tex].
Therefore, the choice that is equivalent to the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is B. [tex]\(4\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The expression inside the square root can be broken down:
[tex]\[
50 = 25 \times 2
\][/tex]
Since [tex]\(25\)[/tex] is a perfect square, we can write:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}
\][/tex]
2. Substitute [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex]:
Our original expression becomes:
[tex]\[
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}
\][/tex]
3. Simplify the expression:
Factor out [tex]\(\sqrt{2}\)[/tex] from both terms:
[tex]\[
5\sqrt{2} - \sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Now, compare this with the given choices:
- A. 5 is just a number and not equivalent to [tex]\(4\sqrt{2}\)[/tex].
- B. [tex]\(4\sqrt{2}\)[/tex] matches exactly with the simplified expression.
- C. [tex]\(\sqrt{48}\)[/tex] simplifies to:
[tex]\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\][/tex]
This is different from [tex]\(4\sqrt{2}\)[/tex].
- D. [tex]\(24\sqrt{2}\)[/tex] is much larger than [tex]\(4\sqrt{2}\)[/tex].
Therefore, the choice that is equivalent to the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] is B. [tex]\(4\sqrt{2}\)[/tex].