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Find the smallest number which multiples 7744 so that the product be a perfect vube​

Answer»

QUESTION :- find the smallest number which multiples 7744 so that the PRODUCT be a perfect cube ?

Answer :--

Lets do Prime FACTORIZATION of 7744 first ,

→ 7744 = ( 2 * 2 * 2) * (2 * 2 * 2) * 11 * 11

Now, as we can see that, 2 and 2 pairs are of 3 , and 11*11 is left with unpair ,

so, we can say that, if we PUT one more 11 their, it will be a perfect cube of = 2 * 2 * 11 . .

So, our Required answer is = 11 .

If we Multiply 7744 with 11 , it will MAKE a perfect cube of = 2 * 2 * 11 = 44 .

11 (Ans).



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