Question : The value of $\sqrt{11+2 \sqrt{18}}$ is closest to:
Option 1: 4.8
Option 2: 4.4
Option 3: 3.8
Option 4: 4.1
Correct Answer: 4.4
Solution :
Given: The expression is $\sqrt{11+2 \sqrt{18}}$
Use the algebraic identity, $(a+b)^2=a^2+b^2+2ab$
$\sqrt{11+2 \sqrt{18}}$
$=\sqrt{({\sqrt9})^2+({\sqrt 2})^2+2\times \sqrt{9}\times \sqrt2}$
$=\sqrt{({\sqrt 9}+{\sqrt 2})^2}$
$={\sqrt 9}+{\sqrt 2}$
$=3+1.414=4.414$
Hence, the correct answer is 4.4.
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