Question

Divide the number 26244 by the smallest number so that the question is a perfect cube . Also find the cube root of quotient.

Answer 1

Hey mate:-

Answer:-

26244\2=13122

13122\2=6561

6561\3=2187

2187\3=729

729\3=243

243\3=81

81\3=27

27\3=9

9\3=3

so

${2} ^{2} {3}^{8}$

So To become a cube, all the prime factors of it must

be to a power which is a multiple of 3

So we have to multiply

${2} ^{2} {3}^{8}$

by

${2}^{1} {3}^{1}$

so that it will become 2^3 3^9 and both prime bases 2 and 3

will be raised to powers (exponents) which are both multiples of 3.

So the cube root of 2^3 3^9 was divided

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.