6 AM Quiz (11 June 2011)... There are more than one way!

What number multiplied by itself is equal to the product of 32 and 162?

There are 2 or more ways to solve this problem. Describe at least 2 methods :)

24 comments:

  1. Method 1:
    32*162=5 184
    √5 184=72


    Method 2:
    guess and check:
    32*162=5 184
    1*1=1
    2*2=4
    3*3=6
    4*4=16
    5*5=25
    6*6=36
    7*7=49
    8*8=64
    ..
    ..
    ..
    72*72=5 184

    ReplyDelete
  2. Therefore, the answer is 72.

    Ishani[04]

    ReplyDelete
  3. 1. Product of 32 and 162 = 5184
    Square root of 5184 = 72
    Check:72*72 = 5184

    2. Prime factorisation of 32 = 2^5
    Prime factorisation of 162 = 2*3^4
    Square root of 2^6*3^4 = Square root of 72*72
    = 72

    ReplyDelete
  4. Method 1: 32x162= 5148
    Square root 5148= 72

    Method 2: Prime factorisation of 32= 2^2^2^2^2
    Prime factorisation of 162= 2^3^3^3^3
    2^6= 64
    3^4= 81
    81-64= 17
    Median of 1~17= 9
    81-9=72 (Not useful as 64+9= 73, which the mean of 72 and 73 would be 72.5)

    Chan Shawn Kit(10)

    ReplyDelete
  5. 32*162=5148

    1. Square root of 5148 = 72
    72*72=5148

    2. Prime factorisation of 32 and 162.
    32 = 2*2*2*2*2
    = 2^5
    162 = 2*3*3*3*3
    = 2*3^4
    2^5*2*3^4=2^6*3^4
    When 2^6*3^4 is square rooted, it will be 2^3*3^2 which equals to 72.

    Gladys 03

    ReplyDelete
  6. Prime factorisation: 32=2*2*2*2*2
    =2^5
    162=2*3*3*3*3
    =2*3^4
    32*162=2^6*3^4
    =(2^3*3^2)*(2^3*3^2)
    2^3*3^2=8*9
    =72

    Square root: 32*162=5148
    The square root of 5148 is 72 threfore, 72*72 is 5148.

    ReplyDelete
  7. 32*162=5148
    The square root of 5148 is 72.
    72 is the answer.

    Ding Nina Lin

    ReplyDelete
  8. M E T H O D O N E :

    32 x 162 = 5184
    Squareroot 5184 and you'll arrive at 72.

    M E T H O D T W O :

    Prime Factorise 32 and 162:
    32 = 2 x 2 x 2 x 2 x 2
    = 2^5

    162 = 2 x 3 x 3 x 3 x 3
    = 2 x 3^4

    Add both of the Prime Factorisations together:
    (2^5) + (2 x 3^4)
    = 2^6 x 3^4

    Assume that (2^6 x 3^4) is ‘2 sets’. And the ‘2 sets’ would be the product of 32 and 162.
    However, we only want ‘1 set’.

    2 sets = 2^6 x 3^4
    Thus, 1 set = 2^3 x 3^2
    = 72

    ReplyDelete
  9. What number multiplied by itself is equal to the product of 32 and 162?

    Method 1:
    32*162=5184
    √5184=72

    Method 2:
    32=2*2*2*2*2
    162=2*3*3*3*3
    32*162=2*2*2*2*2*2*3*3*3*3
    Also can be presented in this way...
    32*162=(2*2*2*3*3)*(2*2*2*3*3)
    √32*162=2*2*2*3*3
    √32*162=(2^3)*(3^2)
    √32*162=72

    Lovy

    ReplyDelete
  10. Method One :

    32 x 162 = 5184

    Squareroot 5184 and you will get 72.

    Method Two :

    Prime Factorise - 32 and 162

    32 = 2 x 2 x 2 x 2 x 2
    = 2^5
    162 = 2 x 3 x 3 x 3 x 3
    = 2 x 3^4
    162 x 32 = 2^6 x 3^4
    Squareroot (2^6 x 3^4)
    = 2^3 x 3^2
    = 8 x 9
    72

    ReplyDelete
  11. Method One :

    Find the product of 32 and 162 . 32*162=5184
    Square root the product which is 5184 and you will get 72 .

    Ans : 72

    Method Two :

    Prime Factorisation Method.

    Prime Factorise 32 and 162.

    32=2*2*2*2*2
    = 2^5

    162= 2*3*3*3*3
    = 2*3^4

    32*162=2^5 x 2 x 3^4

    Square Root (32*162) = distribute the prime numbers out equally into

    groups of two (2^5 x 2 x 3^4)
    = (2*2*2*3*3) x (2*2*2*3*3)
    = 72 x 72
    Ans : 72 .

    ReplyDelete
  12. Method 1:
    Square Root
    32x162=5184
    √5184=72
    Ans:72
    Method 2:
    32
    / \
    2 16
    / \
    2 8
    / \
    2 4
    / \
    2 2
    162
    / \
    2 81
    / \
    3 27
    / \
    3 9
    / \
    3 3
    32=2^5
    162=2*3^4
    162*32=2^6*3^4
    √2^6*3^4=(2^3*3^2)
    2^3*3^2=72

    ReplyDelete
  13. Method 1

    32x162=5184
    √5184=72
    A.n.s. 72

    Method 2

    32=2*2*2*2*2
    162=2*3*3*3*3
    √(2*2*2*2*2*2*3*3*3*3)=√[(2*2*2*3*3)*(2*2*2*3*3)*]
    =2^3*3^2
    =8*9
    =72
    A.n.s. 72

    ReplyDelete
  14. first method:
    32x162=5184
    √5184=72
    answer:72

    second method:
    prime factorization of:
    32=2*2*2*2*2
    162=2*3*3*3*3
    32*162=2*2*2*2*2*2*3*3*3*3
    square rooting=dividing the number into 2 groups of the same number
    square root of 32*162= answer
    so, (2*2*2*3)*(2*2*2*3)=5184
    2*2*2*3=√5184=72
    answer:72

    ReplyDelete
  15. Method 1
    32*162=5184
    √5184 = 72
    ans: 72
    Method 2
    Prime factorisation
    32=2*2*2*2*2
    162=2*3*3*3*3
    32*162=2*2*2*2*2*2*3*3*3*3
    √32*162=(2*2*2*3*3) * (2*2*2*3*3)
    = 72*72
    ans: 72

    ReplyDelete
  16. method 1:
    32*162 = 5184
    square root of 5184 = 72

    method 2:
    [Using prime factorisation]
    32 = 2*2*2*2*2
    162 = 2*3*3*3*3
    32*162 = 2*2*2*2*2 * 2*3*3*3*3
    square root of 32*162 = (2*2*2*3*3) * (2*2*2*3*3)
    = 72 * 72
    Ans:72

    ReplyDelete
  17. -First Method:

    Find the product of 32 and 162
    =5184

    Square Root the product
    =72

    -Second Method:

    Prime Factorise both of the numbers
    = 2^5, 2x3^4

    Combine them together and square root it
    =2^3x3^2
    =72

    ReplyDelete
  18. method 1:
    32x162 = 5184
    square root of 5184 = 72

    method 2:
    [Using prime factorisation]
    32 = 2x2x2x2x2
    162 = 2x3x3x3x3
    32*162 = 2x2x2x2x2 x 2x3x3x3x3
    32x162 = (2x2x2x3x3) x (2x2x2x3x3)
    = 72 x 72
    Ans:72

    ReplyDelete
  19. 1.Square root

    32x162=5184

    √5184=72

    72x72=5184

    ANS:72

    2.Prime factorisation

    32-2*2*2*2*2

    162-2*3*3*3*3


    32x162=2*2*2*2*2*2*3*3*3*3

    =(2*2*2*3*3)x(2*2*2*3*3)

    =72x72
    ANS:72

    ReplyDelete
  20. What number multiplied by itself is equal to the product of 32 and 162?
    Method 1:
    Multiply 32 and 162 together --> 32x162=5184
    √5184 =72

    Method 2:
    Simplifying both numbers into prime numbers; 32 162
    32=2x2x2x2x2 = 2^5

    162= 2x3x3x3x3 = 2x 3^4

    32x162= 2^5 x 2 x 3^4
    = 2^6 x 3^4

    By classifying them into groups of 2,
    2^6 x 3^4 = (2^3 x 3^2) x (2^3 x 3^2)
    (2^3 x 3^2) = 72

    ReplyDelete
  21. @Ishani: You are right that Guess and Check is another method we could adopt :)
    It would be clearer if you indicated that it was SYSTEMATIC Guess and Check and further describe why you choose to organise the numbers in a certain pattern :)

    @Shawn Kit: How does "Median" come into the picture? Maybe you could help us to make the connection?

    @Toby: We can't "Add" both of the Prime Factorisations together like what you've described: (2^5) + (2 x 3^4)
    Instead, it should be written as
    32 x 162 - (2^5) x (2 x 3^4)

    Indeed, many of you are able to describe the "How" to do the square root using the Prime Factorisation method. On the other hand, only Mavis, Ryan and Owen have explicitly explained how to do the square root, which is, organising the factors into 2 groups. Well Done to all 3 :)

    ReplyDelete
  22. 1) 32*162 = 5184
    Square root of 5184 = 72
    Ans: 72

    2) Prime Factorisation
    Prime factorise 32 and 162
    32=2*2*2*2*2= 2^5
    162=2*3*3*3*3= 2*3^4
    32*162=2^6*3^4

    Then we split them into equal groups.
    2^6*3^4= (2^3*3^4) x (2^3*3^4)
    2*group= 162
    1*group= (2^3*3^4)= 72

    Ans: 72

    ReplyDelete
  23. 1) 32*162 = 5184
    Square root of 5184 = 72

    2)32 = 2^5
    162 = 2*3^4
    2^5*2*3^4=2^6*3^4

    To find the square root of this number, we must split the prime factors into 2 equal groups.
    2^6*3^4=(2^3*3^2) x (2^3*3^2)
    (2^3*3^2) = 72

    Answer: 72

    ReplyDelete