Multiply 26244 by the smallest number so that the product is a perfect cube. What is that number .Also, find the cube root of the product. Step by step explaination.
Answers
Answer:
root of the quotient.
26244
/ \
2 13122
/ \
2 6561
/ \
3 2187
/ \
3 729
/ \
3 243
/ \
3 81
/ \
3 27
/ \
3 9
/ \
3 3
So 26244 = 2238
To become a cube, all the prime factors of it must be to a power which is a multiple of 3.
Notice that the prime number base 2 in the factorization is raised to the 2nd power (exponent), but exponent 2 is NOT a multiple of 3, so we'll have to multiply by the 1st power of 2 so that when we add exponents of 2 we will get 23. Notice also that the prime number base 3 in the factorization is raised to the 8th power (exponent), but exponent 8 is NOT a multiple of 3, so we'll have to multiply by the 1st power of 3 so that when we add exponents of 3 we will get 39.
So we have to multiply by 2131 or 2∙3 or 6 to cause 26244 to become a perfect cube. So we have to multiply 2238 by 2131 so that it will become 2339 and both prime bases 2 and 3 will be raised to powers (exponents) which are both multiples of 3.
So then the cube root of 2339 will be gotten by dividing each exponent by 3, which will give 2133 which is 2∙27 or 54.
That's the same as saying
The 26244 must be multiplied by 6 gives 157464 which is a
perfect cube. It is a perfect cube because 543 = 157464.
And the cube root is 54 because 54∙54∙54 = 157464.
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