Simplification


  1. What is the least number which should be subtracted from 0.000326, to have perfect square ?









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    The given number has 6 decimal places.
    Now,

    i.e. 326 – 2 = 324 Which is a perfect square of 18.
    Therefore, 0.000002 should be subtracted from 0.000326 to make it a perfect square of 0.018.

    Correct Option: B

    The given number has 6 decimal places.
    Now,

    i.e. 326 – 2 = 324 Which is a perfect square of 18.
    Therefore, 0.000002 should be subtracted from 0.000326 to make it a perfect square of 0.018.


  1. The least number that must be subtracted from 63520 to make the result a perfect square is :









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    Obviously, 16 must be subtracted to make the result a perfect square.
    i.e.  63520–16 = √63504 = 252

    Correct Option: A

    Obviously, 16 must be subtracted to make the result a perfect square.
    i.e.  63520–16 = √63504 = 252



  1. 1008 divided by which single digit number gives a perfect square?









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    1008 = 4 × 4 × 3 × 3 × 7

    ∴ 
    1008
    = (4 × 3)2 = (12)2
    7

    Correct Option: D

    1008 = 4 × 4 × 3 × 3 × 7

    ∴ 
    1008
    = (4 × 3)2 = (12)2
    7


  1. The product of two numbers is 45 and their difference is 4. The sum of squares of the two numbers is









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y and x > y.
    ∴  xy = 45
    and x – y = 4
    ∴  x2 + y2 = (x – y)2 + 2xy
    = (4)2 + 2 × 45 = 16 + 90
    = 106

    Correct Option: D

    Let the numbers be x and y and x > y.
    ∴  xy = 45
    and x – y = 4
    ∴  x2 + y2 = (x – y)2 + 2xy
    = (4)2 + 2 × 45 = 16 + 90
    = 106



  1. The sum of a positive integer and its square is 2450. The positive integer is









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    x2 + x = 2450
    ⇒  x (x +1) = 2450 = 49 × 50
    ∴  x = 49

    Correct Option: C

    x2 + x = 2450
    ⇒  x (x +1) = 2450 = 49 × 50
    ∴  x = 49