+0

# cubes and cube roots

0
357
3

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
+85817
+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
Sort:

#1
+26640
+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
+85817
+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
+26640
0

I suspect the questioner had positive integers in mind!

Alan  Jun 3, 2014

### 18 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details