Sunday

December 21, 2014

December 21, 2014

Posted by **Loyd** on Monday, October 5, 2009 at 4:09am.

- arithmetic -
**jim**, Monday, October 5, 2009 at 4:52amThis sounds awkward, but is actually easy. Consider the number 400P. It must end in zero - actually, it must end in 00, since it has 100 as a factor.

Therefore its cube root must end in zero. Check this for yourself: the last digit of a cube can be determined by the last digit of the cube root. 1x1x1 = 2, 2x2x2=8 and so on, regardless of the higher digits.

So for the cube root we're already down to factors of 10 - we only have to look at 10, 20, 30... and their cubes all end in 000 because of the three 10s in the factors.

Does 10 work? No, 1000 is a cube of 10, but 400 doesn't divide evenly.

Now try 20.

- arithmetic -
**PsyDAG**, Monday, October 5, 2009 at 10:09am20 * 20 = 400, so 20 is only the square root of 400, not the cube root.

Unfortunately, I can only tell you that 20 is not the answer, but I do not know the answer. Sorry.

- arithmetic -
**Reiny**, Monday, October 5, 2009 at 10:48am400 = 2x2x2 x 2 x 5x5

every triplet of "same factors" will produce a cube

so to make the right side of the above statement into a perfect cube, we need another 2x2x5 or 20

So let's multiply both sides by 20

400x20 = 2x2x2 x 2x2x2 x5x5x5

400(20) = 8000

400P = 8000

so P = 20

- arithmetic -
**Dr Russ**, Monday, October 5, 2009 at 10:55amI think the easiest is to say the

cuberoot(400P)

=cuberoot(2x2x2x2x5x5xP)

=2cuberoot(2x5x5xP)

for cuberoot(2x5x5xP) to be an integer

then P=2x2x5=20

so why is 20 not the answer?

**Answer this Question**

**Related Questions**

MATH - Find the only positive integer whose cube is the sum of the cubes of ...

Arithmetic Operations - Find a set of 4 distinct positive integers a,b,c,d such ...

Algebra - A.Write and solve an equation to find three consecutive integers with ...

Algebra - A.Write and solve an equation to find three consecutive integers with ...

Plz help me..just one MATH question - The number 1 is both the square of an ...

MATH - Find a positive integer m such that 1/2m is a perfect square and 1/3m is ...

math - Find a positive integer m such that 1 2m is a perfect square and 1 3m is ...

Math - I need help on this question. What is the smallest positive integer n ...

maths - The smallest of three consecutive integers is added to the largest, the ...

maths - The smallest of three consecutive integers is added to the largest, the ...