Simplification


  1. The square root of a positive number less than 100 lies between :









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    Since the numbers between –
    10 and 10 will be single digit and the numbers below 100 will be either one digit or two digit. We know that the square root of one or two digit number is always single digit number. Therefore, required answer is option (3).

    Correct Option: C

    Since the numbers between –
    10 and 10 will be single digit and the numbers below 100 will be either one digit or two digit. We know that the square root of one or two digit number is always single digit number. Therefore, required answer is option (3).


  1. If the number p is 5 more than q and the sum of the squares of p and q is 55, then the product of p and q is









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    p = q + 5
    ⇒  p – q = 5
    p2 + q2 = 55
    ∴  (p – q)2 + 2pq = 55
    ⇒  25 + 2 pq = 55
    ⇒  2 pq = 30
    ⇒  pq = 15

    Correct Option: C

    p = q + 5
    ⇒  p – q = 5
    p2 + q2 = 55
    ∴  (p – q)2 + 2pq = 55
    ⇒  25 + 2 pq = 55
    ⇒  2 pq = 30
    ⇒  pq = 15



  1. What number must be added to the expression 16a2 –12a to make it a perfect square ?









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    a2 – 2ab + b2 = (a – b)2
    ∴ 16a2 – 12a

    = (4a)2 – 2 × 4a ×
    3
    2

    Hence, on adding  
    3
    2=
    9
    ,
    24

    expression will be a perfect square.

    Correct Option: A

    a2 – 2ab + b2 = (a – b)2
    ∴ 16a2 – 12a

    = (4a)2 – 2 × 4a ×
    3
    2

    Hence, on adding  
    3
    2=
    9
    ,
    24

    expression will be a perfect square.


  1. The greatest 4 digit number which is a perfect square, is









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    99 × 99 = 9801

    Correct Option: C

    99 × 99 = 9801



  1. The least integer which should be added to 1000 so as to make it a perfect square is









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    (31)2 < 1000 < 322
    32 × 32 = 1024
    ∴  Required number
    = 1024 – 1000 = 24

    Correct Option: C

    (31)2 < 1000 < 322
    32 × 32 = 1024
    ∴  Required number
    = 1024 – 1000 = 24