Answer :
To solve the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex] by simplifying each square root, follow these steps:
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Break down 40 into factors: [tex]\(40 = 4 \times 10\)[/tex].
- Since 4 is a perfect square, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\)[/tex].
2. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Break down 90 into factors: [tex]\(90 = 9 \times 10\)[/tex].
- Since 9 is a perfect square, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\)[/tex].
3. Combine all terms:
- Now, combine all simplified terms: [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
4. Add the coefficients of [tex]\(\sqrt{10}\)[/tex]:
- [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10} = (2 + 8 + 3)\sqrt{10}\)[/tex].
- This equals [tex]\(13\sqrt{10}\)[/tex].
Therefore, the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex] simplifies to [tex]\(13\sqrt{10}\)[/tex], which means the correct choice is B. [tex]\(13 \sqrt{10}\)[/tex].
1. Simplify [tex]\(\sqrt{40}\)[/tex]:
- Break down 40 into factors: [tex]\(40 = 4 \times 10\)[/tex].
- Since 4 is a perfect square, [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\)[/tex].
2. Simplify [tex]\(\sqrt{90}\)[/tex]:
- Break down 90 into factors: [tex]\(90 = 9 \times 10\)[/tex].
- Since 9 is a perfect square, [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\)[/tex].
3. Combine all terms:
- Now, combine all simplified terms: [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10}\)[/tex].
4. Add the coefficients of [tex]\(\sqrt{10}\)[/tex]:
- [tex]\(2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10} = (2 + 8 + 3)\sqrt{10}\)[/tex].
- This equals [tex]\(13\sqrt{10}\)[/tex].
Therefore, the expression [tex]\(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\)[/tex] simplifies to [tex]\(13\sqrt{10}\)[/tex], which means the correct choice is B. [tex]\(13 \sqrt{10}\)[/tex].