Answer :
To solve the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], let's simplify each square root.
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that 50 can be expressed as the product of 25 and 2, i.e., [tex]\(50 = 25 \times 2\)[/tex].
- The square root of a product can be broken down as [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- Since 25 is a perfect square, [tex]\(\sqrt{25} = 5\)[/tex].
- Therefore, [tex]\(\sqrt{50} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(5\sqrt{2}\)[/tex]:
- When you have like terms involving square roots, you can subtract them just like algebraic terms. Here, [tex]\(5\sqrt{2} - \sqrt{2}\)[/tex] can be calculated by considering how many [tex]\(\sqrt{2}\)[/tex]'s you have.
- Think of [tex]\(5\sqrt{2}\)[/tex] as "five individual [tex]\(\sqrt{2}\)[/tex]s" and [tex]\(\sqrt{2}\)[/tex] as one [tex]\(\sqrt{2}\)[/tex].
- Subtract one [tex]\(\sqrt{2}\)[/tex] from five [tex]\(\sqrt{2}\)[/tex]: [tex]\(5\sqrt{2} - 1\sqrt{2} = 4\sqrt{2}\)[/tex].
Thus, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex].
The correct choice is C: [tex]\(4\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that 50 can be expressed as the product of 25 and 2, i.e., [tex]\(50 = 25 \times 2\)[/tex].
- The square root of a product can be broken down as [tex]\(\sqrt{50} = \sqrt{25 \times 2}\)[/tex].
- Since 25 is a perfect square, [tex]\(\sqrt{25} = 5\)[/tex].
- Therefore, [tex]\(\sqrt{50} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\)[/tex].
2. Subtract [tex]\(\sqrt{2}\)[/tex] from [tex]\(5\sqrt{2}\)[/tex]:
- When you have like terms involving square roots, you can subtract them just like algebraic terms. Here, [tex]\(5\sqrt{2} - \sqrt{2}\)[/tex] can be calculated by considering how many [tex]\(\sqrt{2}\)[/tex]'s you have.
- Think of [tex]\(5\sqrt{2}\)[/tex] as "five individual [tex]\(\sqrt{2}\)[/tex]s" and [tex]\(\sqrt{2}\)[/tex] as one [tex]\(\sqrt{2}\)[/tex].
- Subtract one [tex]\(\sqrt{2}\)[/tex] from five [tex]\(\sqrt{2}\)[/tex]: [tex]\(5\sqrt{2} - 1\sqrt{2} = 4\sqrt{2}\)[/tex].
Thus, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex].
The correct choice is C: [tex]\(4\sqrt{2}\)[/tex].