Answer:
Option 2 i.e. 9√2 is the correct option.
Step-by-step explanation:
Given the expression
[tex](\sqrt{200}\:+\:\sqrt{128})[/tex]
The half of [tex](\sqrt{200}\:+\:\sqrt{128})[/tex] can be determined by dividing the expression in half.
Therefore, we need to solve the expression such as
[tex]\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}[/tex]
as
[tex]\sqrt{200}=\sqrt{100\times 2}=\sqrt{100^2\times \:2}=10\sqrt{2}[/tex]
[tex]\sqrt{128}=\sqrt{64\times 2}=\sqrt{8^2\times \:2}=8\sqrt{2}[/tex]
so the expression becomes
[tex]\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}=\frac{10\sqrt{2}+8\sqrt{2}}{2}[/tex]
Add similar elements: [tex]10\sqrt{2}+8\sqrt{2}=18\sqrt{2}[/tex]
[tex]=\frac{18\sqrt{2}}{2}[/tex]
Divide the numbers: 18/2 = 9
[tex]=9\sqrt{2}[/tex]
Therefore, we conclude that:
[tex]\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}=9\sqrt{2}[/tex]
Hence, option 2 i.e. 9√2 is the correct option.
