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# cubes and cube roots

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532
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by which smallest number 33275 can be multiplied so that the result is a perfect cube.also find the cube root for the resulting cube

Guest Jun 2, 2014

#2
+93025
+5

Well...I could multiply by (1/25) and that would give us

33275 *(1/25) = 1331 and that's a perfect cube of 11

Or...I could multiply by 0   and that would give us

33275 * 0 = 0    and that's the perfect cube of 0

Or...I could multiply by -5 and that would give us

-166375 and that's a perfect cube of (-55)

Is this what you were asking??.....Is there a "smallest" number??

CPhill  Jun 2, 2014
#1
+27246
+5

First look at the prime factors of 33275

$${factorize}{\left({\mathtt{33\,275}}\right)} \Rightarrow \left\{ \begin{array}{l}{\mathtt{25}} = {{\mathtt{5}}}^{{\mathtt{2}}}\\ {\mathtt{1\,331}} = {{\mathtt{11}}}^{{\mathtt{3}}}\\ \end{array} \right\}$$

i.e. $$33275=5^2*11^3$$

This should give you a clue.

Alan  Jun 2, 2014
#2
+93025
+5

Well...I could multiply by (1/25) and that would give us

33275 *(1/25) = 1331 and that's a perfect cube of 11

Or...I could multiply by 0   and that would give us

33275 * 0 = 0    and that's the perfect cube of 0

Or...I could multiply by -5 and that would give us

-166375 and that's a perfect cube of (-55)

Is this what you were asking??.....Is there a "smallest" number??

CPhill  Jun 2, 2014
#3
+27246
0

I suspect the questioner had positive integers in mind!

Alan  Jun 3, 2014