Answer :
Let's simplify the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex] step-by-step:
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- We know that 40 can be factored into 4 and 10: [tex]\(\sqrt{40} = \sqrt{4 \times 10}\)[/tex].
- [tex]\(\sqrt{4}\)[/tex] is 2, so [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex].
2. 8[tex]\(\sqrt{10}\)[/tex] stays the same:
- This term is already simplified as [tex]\(8\sqrt{10}\)[/tex].
3. Simplify [tex]\(\sqrt{90}\)[/tex]:
- 90 can be factored into 9 and 10: [tex]\(\sqrt{90} = \sqrt{9 \times 10}\)[/tex].
- [tex]\(\sqrt{9}\)[/tex] is 3, so [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex].
Now, let's combine all the like terms:
- We have [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
Next, add the coefficients of [tex]\(\sqrt{10}\)[/tex]:
- [tex]\(2 + 8 + 3 = 13\)[/tex].
So the expression simplifies to:
- [tex]\(13\sqrt{10}\)[/tex].
Therefore, the choice equivalent to the expression is:
B. [tex]\(13\sqrt{10}\)[/tex].
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- We know that 40 can be factored into 4 and 10: [tex]\(\sqrt{40} = \sqrt{4 \times 10}\)[/tex].
- [tex]\(\sqrt{4}\)[/tex] is 2, so [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex].
2. 8[tex]\(\sqrt{10}\)[/tex] stays the same:
- This term is already simplified as [tex]\(8\sqrt{10}\)[/tex].
3. Simplify [tex]\(\sqrt{90}\)[/tex]:
- 90 can be factored into 9 and 10: [tex]\(\sqrt{90} = \sqrt{9 \times 10}\)[/tex].
- [tex]\(\sqrt{9}\)[/tex] is 3, so [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex].
Now, let's combine all the like terms:
- We have [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
Next, add the coefficients of [tex]\(\sqrt{10}\)[/tex]:
- [tex]\(2 + 8 + 3 = 13\)[/tex].
So the expression simplifies to:
- [tex]\(13\sqrt{10}\)[/tex].
Therefore, the choice equivalent to the expression is:
B. [tex]\(13\sqrt{10}\)[/tex].