College

Which choice is equivalent to the expression below?

[tex]\sqrt{40} + 8\sqrt{10} + \sqrt{90}[/tex]

A. [tex]18\sqrt{10}[/tex]
B. [tex]7\sqrt{10}[/tex]
C. [tex]13\sqrt{10}[/tex]
D. [tex]10\sqrt{10}[/tex]

Answer :

Let's simplify the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex].

1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- The factors of 40 are [tex]\(4 \times 10\)[/tex].
- We can break this down as [tex]\(\sqrt{4 \times 10}\)[/tex].
- This becomes [tex]\(\sqrt{4} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we have [tex]\(2\sqrt{10}\)[/tex].

2. Simplify [tex]\(\sqrt{90}\)[/tex]:
- The factors of 90 are [tex]\(9 \times 10\)[/tex].
- We can break this down as [tex]\(\sqrt{9 \times 10}\)[/tex].
- This becomes [tex]\(\sqrt{9} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we have [tex]\(3\sqrt{10}\)[/tex].

3. Combine all terms:
- Now, substitute back into the original expression:
[tex]\[
\sqrt{40} + 8\sqrt{10} + \sqrt{90} = 2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}
\][/tex]
- Combine all the terms with [tex]\(\sqrt{10}\)[/tex]:
- [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10} = (2 + 8 + 3)\sqrt{10}\)[/tex]
- Simplify the coefficients: [tex]\(13\sqrt{10}\)[/tex].

So, the expression is equivalent to [tex]\(13\sqrt{10}\)[/tex].

The correct answer is: C. [tex]\(13 \sqrt{10}\)[/tex].