### 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 :)

1. Method 1:
32 X 162 = 5184
square root of 5184 = 72
Method 2:
Let y be the number.
y X y = y ^2
y^2 = 32 X 162
y^2 = 5184
72^2 = 5184

2. Method 1: We multiply the 2 values by each other to get the product. 32x162=5184 Next, we take the square root of 5184 which is 72*.

Method 2: We can prime factorise the 2 values and get the HCF, then we can find a number that has a common HCF with these 2 numbers and is also a multiple of 5184, then we can multiply it by itself and see if it is correct.

3. Method 1:
32 X 162 = 5184
square root of 5184 = 72
Method 2 :
Prime factorisation of 32 and 162 is 2^5 and 2 x 3^4
so when u multiply them it will get 2^6 X 3^4
so the square root of 2^6 X 3^4 = 2^3 X 3^2
= 72

4. 1. 32 X 162 = 5184
5184 = 72 * 72
2.The prime factorisation of 32 and 162 is 2^5 and 2 * 3^4
so when you multiply them it will get 2^6 * 3^4
and 2^6 X 3^4 = 2^3 * 3^2= 72

5. 1. The first method is to take 32 x 162 to get the product of 5184. After that, take 5184 and square root it. the answer produced would be 72.

2. The second method is to prime factorise the numbers 32 and 162 which will give 2^5 and 2x3^4 respectively and is equal to 2^6x3^4. To get the answer, grouping can be used. (2^3x3^2)(2^3x3^2) is still equal to 2^6x3^4. Answer is 2^3x3^2 which is 72.

6. Method 1:
32X162=5184
square root of 5184= 72

Method 2:
prime factorization of 32= 2^5
prime factorization or 162= 2*3^4
(2^6X3^2)=(2^3X3^2)X(2^3X3^2)
(2^3X3^2)=72

7. Oops too late D:

Method 1:
32 X 162 = 5184
Square root of 5184 = 72

Method 2:
Prime Factorization of 32 and 162 leads to 3 sets of (2^3X3^2)
= 72

8. Method 1:
Multiply 32 with 162, which equals to 5148, then square root 5148 to get 72.

or

Method 2:
Prime factorise the two numbers 32 and 162, which equals to (2^5) X (2x 3^4)
Then multiply them together, which will equals to (2^6 x 3^4) and that equals to 72. Same answer.

(>< late)

9. method 1: multiply 32 and 162 and square root the answer and you will get 72

method 2:Prime factorise both numbers and find the LCM which will be (2^6*3^4) which will equate to 72 again.

10. This comment has been removed by the author.

11. 1st Method:
32 x 162 = 5184
5184 (Squareroot) = 72

2nd Method:
32 and 162 (Prime Factorise) = 2^6 x 3^4 (Squareroot) = 72

3rd Method:
Repeatedly press the calculator and hope for the right digit :D

12. Method 1: Find Square Root of product
_________
_} 32x162

=72 (Ans)

Method 2: Prime factorise then find cube root

32 and 162 = (2^3 x 3^2) x 3

(2^3 x 3^2) = 72 (Ans)

13. Method 1 is direct, and the answer could be easily evaluated using the calculator. All of you were correct :)

For method 2, all of you also pointed out correctly that we could use Prime Factorisation method. This becomes very handy when calculator is not available. More importantly, it checks our understanding:

To find square root of a number, the Prime factors could be organised into 2 groups.

>> Mervin & "Mitsunari Ishida": Why expressed the factors in 3 groups?
>> Luke: How does HCF come into the picture?

>> Ben: When repeating pressing the calculator, would you be doing it in some systematic way? If you could describe that, it could be one method, too :)

Amongst those who describe the Prime Factorisation method, Amelia is the first who have described the concept behind the square root. Well done :)