Answer :
To simplify the expression [tex]\(\sqrt{40} + 8 \sqrt{10} + \sqrt{90}\)[/tex], let's break it down into simpler parts.
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Notice that 40 can be expressed as a product of a perfect square and another number: [tex]\(40 = 4 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \sqrt{10}\)[/tex].
2. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Similarly, 90 can be expressed as [tex]\(90 = 9 \times 10\)[/tex].
- So, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3 \sqrt{10}\)[/tex].
3. Combine all the terms:
- We have simplified [tex]\(\sqrt{40}\)[/tex] as [tex]\(2 \sqrt{10}\)[/tex] and [tex]\(\sqrt{90}\)[/tex] as [tex]\(3 \sqrt{10}\)[/tex].
- Adding these to [tex]\(8 \sqrt{10}\)[/tex], we get:
[tex]\[
2 \sqrt{10} + 8 \sqrt{10} + 3 \sqrt{10} = (2 + 8 + 3) \sqrt{10} = 13 \sqrt{10}
\][/tex]
Thus, the expression simplifies to [tex]\(13 \sqrt{10}\)[/tex].
The correct answer is:
C. [tex]\(13 \sqrt{10}\)[/tex]
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Notice that 40 can be expressed as a product of a perfect square and another number: [tex]\(40 = 4 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \sqrt{10}\)[/tex].
2. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Similarly, 90 can be expressed as [tex]\(90 = 9 \times 10\)[/tex].
- So, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3 \sqrt{10}\)[/tex].
3. Combine all the terms:
- We have simplified [tex]\(\sqrt{40}\)[/tex] as [tex]\(2 \sqrt{10}\)[/tex] and [tex]\(\sqrt{90}\)[/tex] as [tex]\(3 \sqrt{10}\)[/tex].
- Adding these to [tex]\(8 \sqrt{10}\)[/tex], we get:
[tex]\[
2 \sqrt{10} + 8 \sqrt{10} + 3 \sqrt{10} = (2 + 8 + 3) \sqrt{10} = 13 \sqrt{10}
\][/tex]
Thus, the expression simplifies to [tex]\(13 \sqrt{10}\)[/tex].
The correct answer is:
C. [tex]\(13 \sqrt{10}\)[/tex]