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    Bank Exam

    Topic

    Shajalal Islami Bank Ltd. - Trainee Senior Officer - 2016

    What is the difference between 150\sqrt {150} and 54\sqrt {54} ?

    ক)
    \(2\sqrt 6 \)
    খ)
    \(16\sqrt 6 \)
    গ)
    \(9\sqrt 6 \)
    ঘ)
    \(6\sqrt 2 \)

    Explanation

    Solution: প্রথমে প্রতিটি সংখ্যাকে মৌলিক সংখ্যার গুণ আকারে প্রকাশ করি । 150 =(3×50) =3 ×50 =3 ×2 ×\sqrt {150}  = \sqrt {(3 \times 50)}  = \sqrt 3  \times \sqrt {50}  = \sqrt 3  \times \sqrt 2  \times 25 =5×3 ×2 =56\sqrt {25}  = 5 \times \sqrt 3  \times \sqrt 2  = 5\sqrt 6 54 =(2×27) =2 ×27 =2 ×3 ×\sqrt {54}  = \sqrt {(2 \times 27)}  = \sqrt 2  \times \sqrt {27}  = \sqrt 2  \times \sqrt 3  \times 9 =3×2 ×3 =36\sqrt 9  = 3 \times \sqrt 2  \times \sqrt 3  = 3\sqrt 6 So 150 −54 =56 −36 =26\sqrt {150}  - \sqrt {54}  = 5\sqrt 6  - 3\sqrt 6  = 2\sqrt 6 Shortcut: 150 −54 =6×25 −6×9\sqrt {150}  - \sqrt {54}  = \sqrt {6 \times 25}  - \sqrt {6 \times 9} 6×(5)2   −6×(3)2   =56 −36 =26\sqrt {6 \times {{(5)}^{2\;}}}  - \sqrt {6 \times {{(3)}^{2\;}}}  = 5\sqrt 6  - 3\sqrt 6  = 2\sqrt 6

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