Find the simplest value of \[ 2\sqrt{50} + \sqrt{18} - \sqrt{72} \] (given \( \sqrt{2} = 1.414 \)).

নিম্নলিখিত রাশিটির সরলতম মান নির্ণয় করো: \[ 2\sqrt{50} + \sqrt{18} - \sqrt{72} \] (যেখানে \( \sqrt{2} = 1.414 \)).

Practice MCQ for SSC, UPSC, RRB Exams

A. \( 9.898 \) A. \( 9.898 \)
B. \( 10.312 \) B. \( 10.312 \)
C. \( 8.484 \) C. \( 8.484 \)
D. \( 4.242 \) D. \( 4.242 \)

Correct Answer: A সঠিক উত্তর: A

Explanation ব্যাখ্যা

Simplify each radical:

\[ \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \]

\[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \]

\[ \sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2} \]

Now substitute:

\[ 2(5\sqrt{2}) + 3\sqrt{2} - 6\sqrt{2} \]

\[ = 10\sqrt{2} + 3\sqrt{2} - 6\sqrt{2} \]

\[ = 7\sqrt{2} \]

Using \( \sqrt{2} = 1.414 \):

\[ 7 \times 1.414 = 9.898 \]

Correct Answer: Option A — \( 9.898 \)

প্রতিটি মূল সরল করি:

\[ \sqrt{50} = 5\sqrt{2}, \quad \sqrt{18} = 3\sqrt{2}, \quad \sqrt{72} = 6\sqrt{2} \]

তাহলে,

\[ 2(5\sqrt{2}) + 3\sqrt{2} - 6\sqrt{2} = 7\sqrt{2} \]

\[ = 7 \times 1.414 = 9.898 \]

সঠিক উত্তর: Option A — \( 9.898 \)

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