High School

Which choice is equivalent to the expression below?

[tex]\sqrt{50} - \sqrt{2}[/tex]

A. [tex]4 \sqrt{2}[/tex]
B. [tex]24 \sqrt{2}[/tex]
C. 5
D. [tex]\sqrt{48}[/tex]

Answer :

To solve the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], let's simplify [tex]\(\sqrt{50}\)[/tex] first:

1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that 50 can be rewritten as [tex]\(25 \times 2\)[/tex].
- This means [tex]\(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2}\)[/tex].
- Since [tex]\(\sqrt{25} = 5\)[/tex], it follows that [tex]\(\sqrt{50} = 5 \times \sqrt{2}\)[/tex].

2. Substitute Back into the Expression:
- Replace [tex]\(\sqrt{50}\)[/tex] in the original expression with [tex]\(5\sqrt{2}\)[/tex].
- The expression now becomes [tex]\(5\sqrt{2} - \sqrt{2}\)[/tex].

3. Combine the Like Terms:
- Both terms contain [tex]\(\sqrt{2}\)[/tex], so you can factor out [tex]\(\sqrt{2}\)[/tex].
- This gives [tex]\( (5 - 1) \sqrt{2} = 4 \sqrt{2} \)[/tex].

Therefore, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4 \sqrt{2}\)[/tex]. The correct choice is A: [tex]\(4 \sqrt{2}\)[/tex].