Answer :
To solve the problem and find which choice is equivalent to the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], we can follow these steps:
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that 50 can be broken down into a product of its factors: [tex]\(50 = 25 \times 2\)[/tex].
- Since 25 is a perfect square, we can simplify [tex]\(\sqrt{50}\)[/tex] as follows:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}
\][/tex]
2. Calculate [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
- Now, we substitute the simplified form of [tex]\(\sqrt{50}\)[/tex]:
[tex]\[
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}
\][/tex]
- Since both terms have [tex]\(\sqrt{2}\)[/tex] in them, we can combine them:
[tex]\[
5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Thus, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex].
Therefore, the correct choice is B. [tex]\(4\sqrt{2}\)[/tex].
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
- Notice that 50 can be broken down into a product of its factors: [tex]\(50 = 25 \times 2\)[/tex].
- Since 25 is a perfect square, we can simplify [tex]\(\sqrt{50}\)[/tex] as follows:
[tex]\[
\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2}
\][/tex]
2. Calculate [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
- Now, we substitute the simplified form of [tex]\(\sqrt{50}\)[/tex]:
[tex]\[
\sqrt{50} - \sqrt{2} = 5\sqrt{2} - \sqrt{2}
\][/tex]
- Since both terms have [tex]\(\sqrt{2}\)[/tex] in them, we can combine them:
[tex]\[
5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
Thus, the expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex] simplifies to [tex]\(4\sqrt{2}\)[/tex].
Therefore, the correct choice is B. [tex]\(4\sqrt{2}\)[/tex].