Q44 / 160 · TS EAMCET 2023 (12 May Shift 2) · Mathematics

$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|=$

  • A
    $5 \sqrt{2}-3 \sqrt{3}$
  • B
    $5 \sqrt{3}-3 \sqrt{5}$
  • C
    $10 \sqrt{3}-15 \sqrt{2}$
  • Correct answer
    D
    $15 \sqrt{2}-25 \sqrt{3}$

Solution

$\left|\begin{array}{ccc}\sqrt{3} & 2 \sqrt{5} & \sqrt{5} \\ \sqrt{15} & 5 & \sqrt{10} \\ 3 & \sqrt{15} & 5\end{array}\right|$ $\begin{aligned} & =\sqrt{3}(25-\sqrt{150})-2 \sqrt{5}(5 \sqrt{15}-3 \sqrt{10})+\sqrt{5}(15-15) \\ & =25 \sqrt{3}-15 \sqrt{2}-50 \sqrt{3}+30 \sqrt{2} \\ & =15 \sqrt{2}-25 \sqrt{3}\end{aligned}$

Hence, the correct answer is option: 'D'.

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