Answer :
To solve the expression [tex]\(\sqrt{40} + 2\sqrt{10} + \sqrt{90}\)[/tex], we can simplify the square roots first:
1. Simplifying [tex]\(\sqrt{40}\)[/tex]:
- The number 40 can be expressed as [tex]\(4 \times 10\)[/tex].
- [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\)[/tex].
2. Simplifying [tex]\(\sqrt{90}\)[/tex]:
- The number 90 can be expressed as [tex]\(9 \times 10\)[/tex].
- [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\)[/tex].
Now, substitute these simplified values back into the original expression:
- [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex]
- [tex]\(2\sqrt{10}\)[/tex] (already in its simplest form)
- [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex]
Combine all of these:
[tex]\[
2\sqrt{10} + 2\sqrt{10} + 3\sqrt{10}
\][/tex]
Combine the like terms:
[tex]\[
(2 + 2 + 3)\sqrt{10} = 7\sqrt{10}
\][/tex]
Therefore, the expression simplifies to [tex]\(7\sqrt{10}\)[/tex]. The correct choice is:
A. [tex]\(7\sqrt{10}\)[/tex]
1. Simplifying [tex]\(\sqrt{40}\)[/tex]:
- The number 40 can be expressed as [tex]\(4 \times 10\)[/tex].
- [tex]\(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\)[/tex].
2. Simplifying [tex]\(\sqrt{90}\)[/tex]:
- The number 90 can be expressed as [tex]\(9 \times 10\)[/tex].
- [tex]\(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\)[/tex].
Now, substitute these simplified values back into the original expression:
- [tex]\(\sqrt{40} = 2\sqrt{10}\)[/tex]
- [tex]\(2\sqrt{10}\)[/tex] (already in its simplest form)
- [tex]\(\sqrt{90} = 3\sqrt{10}\)[/tex]
Combine all of these:
[tex]\[
2\sqrt{10} + 2\sqrt{10} + 3\sqrt{10}
\][/tex]
Combine the like terms:
[tex]\[
(2 + 2 + 3)\sqrt{10} = 7\sqrt{10}
\][/tex]
Therefore, the expression simplifies to [tex]\(7\sqrt{10}\)[/tex]. The correct choice is:
A. [tex]\(7\sqrt{10}\)[/tex]