Question

3) The half of (√200 + √128 ) is

1. √100 + √64

2. 9√2

3. 18√2

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Answer 1

Answer:

Option 2 i.e. 9√2 is the correct option.

Step-by-step explanation:

Given the expression

$(\sqrt{200}\:+\:\sqrt{128})$

The half of $(\sqrt{200}\:+\:\sqrt{128})$ can be determined by dividing the expression in half.

Therefore, we need to solve the expression such as

$\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}$

as

$\sqrt{200}=\sqrt{100\times 2}=\sqrt{100^2\times \:2}=10\sqrt{2}$

$\sqrt{128}=\sqrt{64\times 2}=\sqrt{8^2\times \:2}=8\sqrt{2}$

so the expression becomes

$\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}=\frac{10\sqrt{2}+8\sqrt{2}}{2}$

Add similar elements:  $10\sqrt{2}+8\sqrt{2}=18\sqrt{2}$

                     $=\frac{18\sqrt{2}}{2}$

Divide the numbers: 18/2 = 9

                      $=9\sqrt{2}$

Therefore, we conclude that:

$\frac{\left(\sqrt{200}\:+\:\sqrt{128}\:\right)}{2}=9\sqrt{2}$

Hence, option 2 i.e. 9√2 is the correct option.