ABC26GN1412 · Square Roots and Cube Roots

Subject: General Aptitude · Chapter: Square Roots and Cube Roots · Exam: 2003 · Marks: · Difficulty:

If $a=0.1039$, then the value of $\sqrt{4 a^{2}-4 a+1}+3 a$ is
(a)0.1039
(b)0.2078
(c)1.1039
(d)2.1039
Answer
Answer (as printed): C
Explanation
$$\begin{aligned} \sqrt{4 a^{2}-4 a+1} & +3 a \\ = & \sqrt{(1)^{2}+(2 a)^{2}-2 \times 1 \times 2 a}+3 a=\sqrt{(1-2 a)^{2}}+3 a \\ = & (1-2 a)+3 a=(1+a)=(1+0.1039)=1.1039 \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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