Discussion
The value of \(\frac{\sqrt{5043} \times \sqrt{50}}{\sqrt{32} \times \sqrt{1323}}\) is :
Answer: D
The value is \(\frac{205}{84}\).
Combine under one root and factorise: \(5043 = 3 \times 41^2\), \(1323 = 3^3 \times 7^2\), \(50 = 2 \times 5^2\) and \(32 = 2^5\).
\[ \begin{aligned} \sqrt{\frac{5043 \times 50}{32 \times 1323}} &= \sqrt{\frac{41^2 \times 5^2}{2^4 \times 3^2 \times 7^2}} \\ &= \frac{41 \times 5}{4 \times 3 \times 7} \\ &= \frac{205}{84} \end{aligned} \]
The key step is \(\sqrt{5043} = 41\sqrt{3}\); taking 5043 as \(43^2 \times 3\) leads to 215, and \(\frac{205}{42}\) is exactly twice the true value. Check: \(\sqrt{32} \times \sqrt{1323} = 4\sqrt{2} \times 21\sqrt{3}\) and \(\sqrt{5043} \times \sqrt{50} = 41\sqrt{3} \times 5\sqrt{2}\), so the ratio is \(\frac{205}{84}\).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development