Question

Find the smallest number by which the given number must be
divided so that the quotient has a cube root. Also find the cube
root of the quotient.
(b) 26244
(a) 6655...
(c) 27648​

Answer 1

Answer:

Prime factorising 1296, we get,

1296=2×2×2×2×3×3×3×3

=2

4

×3

4

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 4 and number of 3's is 4.

So we need to divide 2 and 3 from the factorization to make 1296 a perfect cube.

Hence, the smallest number by which 1296 must be divided to obtain a perfect cube is 2×3=6.

Therefore, option B is correct.

Answer 2

Answer:

number must be

divided so that the quotient has a cube root. Also find the cube

root of the quotient.

(b) 26244

(a) 6655... number must be

divided so that the quotient has a cube root. Also find the cube

root of the quotient.

(b) 26244

(a) 6655...

(c) 27648

(c) 27648