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Question 44848: I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I?
I need to explain how I got this
Help
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I am a whole number between 40,000 and 50,000. When I am divided by 2, the asnwer is a perfect square. When I am divided by 3, the answer is a perfect cube. Who am I?
I need to explain how I got this
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Let the number be #; then 40000<#<50000
When # is divided by 3 the result is a perfect cube, as follows:
#/3=y^3
Then #=3y^3
Put that into the inequality, as follows:
40000<3y^3<50000
Divide thru by 3 to get
13333.333< y^3 <16666.666...
Take the cube root from left to right to get:
23.7126...< y <25.5436...
Therefore y is either 24 or 25
Then #=3*24^3 or #=3*25^3
If #=3^24^3=41472
When we divide this by 2 we get 20736
If we take the square root we get 144.
So when 41472 is divided by 2 we DO get a perfect square.
And when we divide 41472 by 3 we DO get a perfect cube.
Could #=3*25^3 also be an acceptable answer?
#=3*25^3= 46875
When we divide by 2 we get 23437.5
which is not a perfect square.
So the number you are looking for is 41472.
Cheers,
Stan H.
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