Answer :
To find an equivalent expression to [tex]\(\sqrt{50} - \sqrt{2}\)[/tex], we can simplify the square root of 50.
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The number 50 can be factored into its prime factors:
[tex]\(50 = 2 \times 5 \times 5 = 2 \times 25\)[/tex].
Now, apply the property of square roots:
[tex]\[
\sqrt{50} = \sqrt{2 \times 25} = \sqrt{2} \times \sqrt{25}
\][/tex]
Since [tex]\(\sqrt{25} = 5\)[/tex], we have:
[tex]\[
\sqrt{50} = 5\sqrt{2}
\][/tex]
2. Substitute back into the expression:
Replace [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex] in the original expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Since these are like terms, you can subtract them:
[tex]\[
5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
This simplified expression is equivalent to the original expression. Therefore, the correct choice is:
D. [tex]\(4 \sqrt{2}\)[/tex]
1. Simplify [tex]\(\sqrt{50}\)[/tex]:
The number 50 can be factored into its prime factors:
[tex]\(50 = 2 \times 5 \times 5 = 2 \times 25\)[/tex].
Now, apply the property of square roots:
[tex]\[
\sqrt{50} = \sqrt{2 \times 25} = \sqrt{2} \times \sqrt{25}
\][/tex]
Since [tex]\(\sqrt{25} = 5\)[/tex], we have:
[tex]\[
\sqrt{50} = 5\sqrt{2}
\][/tex]
2. Substitute back into the expression:
Replace [tex]\(\sqrt{50}\)[/tex] with [tex]\(5\sqrt{2}\)[/tex] in the original expression [tex]\(\sqrt{50} - \sqrt{2}\)[/tex]:
[tex]\[
5\sqrt{2} - \sqrt{2}
\][/tex]
3. Combine like terms:
Since these are like terms, you can subtract them:
[tex]\[
5\sqrt{2} - 1\sqrt{2} = (5 - 1)\sqrt{2} = 4\sqrt{2}
\][/tex]
This simplified expression is equivalent to the original expression. Therefore, the correct choice is:
D. [tex]\(4 \sqrt{2}\)[/tex]