Answer :
We begin by simplifying each square root term.
1. Simplify [tex]$\sqrt{40}$[/tex]:
[tex]$$\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}.$$[/tex]
2. The middle term [tex]$8\sqrt{10}$[/tex] remains as it is.
3. Simplify [tex]$\sqrt{90}$[/tex]:
[tex]$$\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}.$$[/tex]
Now, we add the simplified terms:
[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]$\boxed{13\sqrt{10}}$[/tex], which corresponds to choice D.
1. Simplify [tex]$\sqrt{40}$[/tex]:
[tex]$$\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}.$$[/tex]
2. The middle term [tex]$8\sqrt{10}$[/tex] remains as it is.
3. Simplify [tex]$\sqrt{90}$[/tex]:
[tex]$$\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}.$$[/tex]
Now, we add the simplified terms:
[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]$\boxed{13\sqrt{10}}$[/tex], which corresponds to choice D.