Simplification


  1. If   √0.05 × 0.5 × a = 0.5 × 0.05 × √b, then a/b is equal to









  1. View Hint View Answer Discuss in Forum

    0.05 × 0.5 × a
    = 0.5 × 0.05 × √b
    On squaring both sides,
    0.05 × 0.5 × a = 0.5 × 0.5 × 0.05 × 0.05 × b
    ⇒  a = 0.5 × 0.05b

    ⇒ 
    a
    = 0.5 × 0.05 = 0.025
    b

    Correct Option: B

    0.05 × 0.5 × a
    = 0.5 × 0.05 × √b
    On squaring both sides,
    0.05 × 0.5 × a = 0.5 × 0.5 × 0.05 × 0.05 × b
    ⇒  a = 0.5 × 0.05b

    ⇒ 
    a
    = 0.5 × 0.05 = 0.025
    b


  1. The simplified value of  
    3√2
    4√3
    +
    6
      is
    3 + √66 + √23 + √2









  1. View Hint View Answer Discuss in Forum

    3√2
    6 + √3

    =
    3√2(√6 − √3)
    (√6 + √3)(√6 − √3)

    =
    3√2(√6 − √3)
    6 − 3

    = √2(√6 − √3)
    = √12 − √6
    = 2 √3 − √6
    4√3
    6 + √2

    =
    4√3(√6 − √2)
    (√6 + √2)(√6 − √2)

    =
    4√3(√6 − √2)
    6 − 2

    = √3(√6 − √2)
    = √18 − √6
    = 3√2 − √6
    6
    3 + √2

    =
    6(√3 − √2)
    (√3 + √2)(√3 − √2)

    =
    18 − √12
    3 − 2

    = 3√2 − 2√3
    ∴  Expression
    = 2√3 − √6 − (3√2 − √6) + 3√2 − 2√3
    = 2√3 − √6 − 3√2 + √6 + 3√2 − 2√3 = 0

    Correct Option: D

    3√2
    6 + √3

    =
    3√2(√6 − √3)
    (√6 + √3)(√6 − √3)

    =
    3√2(√6 − √3)
    6 − 3

    = √2(√6 − √3)
    = √12 − √6
    = 2 √3 − √6
    4√3
    6 + √2

    =
    4√3(√6 − √2)
    (√6 + √2)(√6 − √2)

    =
    4√3(√6 − √2)
    6 − 2

    = √3(√6 − √2)
    = √18 − √6
    = 3√2 − √6
    6
    3 + √2

    =
    6(√3 − √2)
    (√3 + √2)(√3 − √2)

    =
    18 − √12
    3 − 2

    = 3√2 − 2√3
    ∴  Expression
    = 2√3 − √6 − (3√2 − √6) + 3√2 − 2√3
    = 2√3 − √6 − 3√2 + √6 + 3√2 − 2√3 = 0



  1. The value of √10−6 × 0.25 is









  1. View Hint View Answer Discuss in Forum

    Expression =√10−6 × 0.25

    0.25
    =
    25
    106106 × 102

    0.25
    =
    5
    108104

    = 0.0005

    Correct Option: B

    Expression =√10−6 × 0.25

    0.25
    =
    25
    106106 × 102

    0.25
    =
    5
    108104

    = 0.0005


  1. A tourist spends daily as many rupees as the number of days of his total tour. If his total expenses were ₹ 361, then how many days did his tour last ?









  1. View Hint View Answer Discuss in Forum

    Let the number of days of tour be x.
    ∴  Total expenditure = x2
    ∴  x2 = 361 ⇒ x = √361 = 19

    Correct Option: B

    Let the number of days of tour be x.
    ∴  Total expenditure = x2
    ∴  x2 = 361 ⇒ x = √361 = 19



  1. 64009 is equal to









  1. View Hint View Answer Discuss in Forum


    ∴  √64009 = 253

    Correct Option: C


    ∴  √64009 = 253