Question : Simplify the following expression.
$0.01+0.68 \times 0.68+0.22 \times 0.22+0.044+0.136+0.44 \times 0.68$
Option 1: $0.69$
Option 2: $1$
Option 3: $0.8$
Option 4: $0.9$
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Correct Answer: $1$
Solution :
$0.01+0.68 \times 0.68+0.22 \times 0.22+0.044+0.136+0.44 \times 0.68$.
$= 0.1^2 + 0.68^2 + 0.22^2 + 2 × 0.1 × 0.22 + 2 × 0.1 × 0.68 + 2 × 0.22 × 0.68$
$= (0.1 + 0.22 + 0. 68)^2$
$= (1)^2$
$= 1$
Hence, the correct answer is $1$.
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