High School Maths Examples and Questions

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Answers − Reducing Surds

  1.   Reduce the surd √28

  2.   Simplify the surd √108

  3.   Reduce the surd √324

(a)  List the perfect squares
   4     9    25     36    49     64     81
(b)  From (a) the GREEN ones below are factors of 324
   4     9    25     36    49     64     81
(c)  From (b) choose the largest perfect square 81
(d)  Carry on as before
       √324 = √(81 × 4) = 9√4
         = 9 × 2 = 18

  4.   Simplify the surd √396

(a)  List the perfect squares
   4     9    25     36    49     64     81
(b)  From (a) the GREEN ones below are factors of 396
   4     9    25     36    49     64     81
(c)  From (b) choose the largest perfect square 36
(d)  Carry on as before
       √396 = √(36 × 11)
         = 6√11

  5.   Reduce the surd √900

(a)  List the perfect squares
   4     9    25     36    49     64    81     100
(b)  From (a) the GREEN ones below are factors of 900
   4     9    25     36    49     64     81     100
(c)  From (b) choose the largest perfect square 100
(d)  Carry on as before
       √900 = √(100 × 9)
         = 10√9 = 10 × 3 = 30

  6.   Simplify the surd √960

(a)  List the perfect squares
   4     9    25     36    49     64     81
(b)  From (a) the GREEN ones below are factors of 960
   4     9    25     36    49     64     81
(c)  From (b) choose the largest perfect square 64
(d)  Carry on as before
       √960 = √(64 × 15)
         = 8√15

  7.   Reduce the surd √5120

(a)  List the perfect squares
   4     9    25     36    49     64     81
(b)  From (a) the GREEN ones below are factors of 5120
   4     9    25     36    49     64     81
(c)  From (b) choose the largest perfect square 64
(d)  Carry on as before
       √5120 = √(64 × 80) = 8√80
         = 8√(4 × 20) = 8.2√20
         = 16√(4 × 5) = 16.2√5
         = 32√5

  8.   Simplify the surd √3675

(a)  List the perfect squares
   4     9    25     36    49     64     81
(b)  From (a) the GREEN ones below are factors of 3675
   4     9    25     36    49     64     81
(c)  From (b) choose the largest perfect square 49
(d)  Carry on as before
       √3675 = √(49 × 75) = 7√75
         = 7√(25 × 3) = 7.5√3
         = 35√3

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