(4+√(7)), expressed as a perfect square, is equal to (Section Officers', 2005) · ABC26GN1957
Subject: General Aptitude · Chapter: Surds and Indices
$(4+\sqrt{7})$, expressed as a perfect square, is equal to (Section Officers', 2005)
(a)$(2+\sqrt{7})^{2}$
(b)$\left(\frac{\sqrt{7}}{2}+\frac{1}{2}\right)^{2}$
(c)$\left\{\frac{1}{2}(\sqrt{7}+1)^{2}\right\}$
(d)$(\sqrt{3}+\sqrt{4})^{2}$
Answer
Explanation
$4+\sqrt{7}=\frac{7}{2}+\frac{1}{2}+2 \times \frac{\sqrt{7}}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=\left(\frac{\sqrt{7}}{\sqrt{2}}\right)^{2}+\left(\frac{1}{\sqrt{2}}\right)^{2}+2 \times \frac{\sqrt{7}}{\sqrt{2}} \times \frac{1}{\sqrt{2}}=\left(\frac{\sqrt{7}}{\sqrt{2}}+\frac{1}{\sqrt{2}}\right)^{2}=\frac{1}{2}(\sqrt{7}+1)^{2}.$
Explanation as extracted from the printed page; notation may be imperfect.
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