Question

Find the smallest number by which 364500 must be divided so that the quotient is a perfect cube

Answer 1

Step-by-step explanation:

4 is the smallest number by which 364500 must be divided so that the quotient is a perfect cube.

Answer 2

Answer:

we have,

364500=2×2×3×3×3×3×5×5×5.

the prime factor 2,3 has no pairs of 3.so,it is not a perfect cube.

if we divide 364500 by 2×2×3.

so we get a perfect cube.

√364500÷2×2×3=√3×3×3×5×5×5

√1093500=√3×3×3×5×5×5

√1093500=3×5

√1093500=15

1093500 is a perfect cube