Simplification


  1. Number of digits in the square root of 62478078 is:









  1. View Hint View Answer Discuss in Forum

    Number of digits in 62478078 = 8
    ∴  Number of digits in its square root = 4
    ⇒  √62478078 ≈ 7904
    ⇒  √62473216 = 7904

    Correct Option: A

    Number of digits in 62478078 = 8
    ∴  Number of digits in its square root = 4
    ⇒  √62478078 ≈ 7904
    ⇒  √62473216 = 7904


  1. The simplified value of  
    32 + √48
      is
    8 + √12









  1. View Hint View Answer Discuss in Forum

    Expression =  
    32 + √48
    8 + √12

    =
    4√2 + 4√3
    =
    4(√2 + √3)
    = 2
    2√2 + 2√32(√2 + √3)

    Correct Option: B

    Expression =  
    32 + √48
    8 + √12

    =
    4√2 + 4√3
    =
    4(√2 + √3)
    = 2
    2√2 + 2√32(√2 + √3)



  1. Simplify :   3
    33
    ÷ 9
    1
    × 23
    1
    6479









  1. View Hint View Answer Discuss in Forum

    Expression =   3
    33
    ÷ 9
    1
    × 23
    1
    6479

    =  
    225
    ÷
    64
    × 2
    28
    6479

    =
    25
    ×
    7
    ×
    28
    × 2
    64649

    =
    5 × 7
    × 2 =
    35
    = 2
    3
    8 × 41616

    Correct Option: D

    Expression =   3
    33
    ÷ 9
    1
    × 23
    1
    6479

    =  
    225
    ÷
    64
    × 2
    28
    6479

    =
    25
    ×
    7
    ×
    28
    × 2
    64649

    =
    5 × 7
    × 2 =
    35
    = 2
    3
    8 × 41616


  1. What is the value of  
    24 + √216
      ?
    96









  1. View Hint View Answer Discuss in Forum

    Expression =
    24 + √216
    96

    =
    2√6 + 6√6
    =
    8√6
    = 2
    4√64√6

    Correct Option: C

    Expression =
    24 + √216
    96

    =
    2√6 + 6√6
    =
    8√6
    = 2
    4√64√6



  1. The number of pairs of natural numbers, the difference of whose squares is 45 will be









  1. View Hint View Answer Discuss in Forum

    Let the numbers be x and y where x > y
    ∴  x2 − y2 = 45
    ⇒  (x + y)(x – y) = 45
    Now, 45 = 5 × 9
    = 15 × 3 = 45 × 1
    ∴  Number of pairs = 3

    Correct Option: B

    Let the numbers be x and y where x > y
    ∴  x2 − y2 = 45
    ⇒  (x + y)(x – y) = 45
    Now, 45 = 5 × 9
    = 15 × 3 = 45 × 1
    ∴  Number of pairs = 3