Question
If $$a = 0.1039{\text{,}}$$ then the value of $$\sqrt {4{a^2} - 4a + 1} $$ $$ + $$ $$3a$$ is ?
Answer: Option C
$$\eqalign{
& = \sqrt {4{a^2} - 4a + 1} + 3a \cr
& = \sqrt {{{\left( 1 \right)}^2} + {{\left( {2a} \right)}^2} - 2 \times 1 \times 2a} + 3a \cr
& = \sqrt {{{\left( {1 - 2a} \right)}^2}} + 3a \cr
& = \left( {1 - 2a} \right) + 3a \cr
& = \left( {1 + a} \right) \cr
& = \left( {1 + 0.1039} \right) \cr
& = 1.1039 \cr} $$
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$$\eqalign{
& = \sqrt {4{a^2} - 4a + 1} + 3a \cr
& = \sqrt {{{\left( 1 \right)}^2} + {{\left( {2a} \right)}^2} - 2 \times 1 \times 2a} + 3a \cr
& = \sqrt {{{\left( {1 - 2a} \right)}^2}} + 3a \cr
& = \left( {1 - 2a} \right) + 3a \cr
& = \left( {1 + a} \right) \cr
& = \left( {1 + 0.1039} \right) \cr
& = 1.1039 \cr} $$
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