Answer :
Let's simplify the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex] step by step:
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Recognize that [tex]\(40 = 4 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we have [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex].
2. Leave [tex]\(8\sqrt{10}\)[/tex] as it is:
- There's nothing to simplify here, so it remains [tex]\(8\sqrt{10}\)[/tex].
3. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Recognize that [tex]\(90 = 9 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we have [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex].
4. Combine all the terms:
- The expression now is [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
- Combine the coefficients of [tex]\(\sqrt{10}\)[/tex]: [tex]\(2 + 8 + 3\)[/tex].
5. Calculate the total coefficient:
- [tex]\(2 + 8 + 3 = 13\)[/tex].
Thus, the simplified expression is [tex]\(13\sqrt{10}\)[/tex].
The choice that matches this is:
C. [tex]\(13\sqrt{10}\)[/tex]
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Recognize that [tex]\(40 = 4 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{4} = 2\)[/tex], we have [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex].
2. Leave [tex]\(8\sqrt{10}\)[/tex] as it is:
- There's nothing to simplify here, so it remains [tex]\(8\sqrt{10}\)[/tex].
3. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Recognize that [tex]\(90 = 9 \times 10\)[/tex].
- Therefore, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10}\)[/tex].
- Since [tex]\(\sqrt{9} = 3\)[/tex], we have [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex].
4. Combine all the terms:
- The expression now is [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
- Combine the coefficients of [tex]\(\sqrt{10}\)[/tex]: [tex]\(2 + 8 + 3\)[/tex].
5. Calculate the total coefficient:
- [tex]\(2 + 8 + 3 = 13\)[/tex].
Thus, the simplified expression is [tex]\(13\sqrt{10}\)[/tex].
The choice that matches this is:
C. [tex]\(13\sqrt{10}\)[/tex]