Respuesta :

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.

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