Q.
Find the smallest number by which 5400 should be multiplied so that the product is a perfect cube. The following steps are involved in solving the above problem. Arrange them in sequential order.
(A) $\Rightarrow 5400=2^3 \times 3^3 \times 5^2$
(B) On prime factorization of 5400 , we get $5400=$ $2 \times 2 \times 2 \times 5 \times 5 \times 3 \times 3 \times 3$.
(C) $\therefore 5400$ must be multiplied by 5 so that the product is a perfect cube.
(D) In the prime factorization of 5400 , we observe that 5 has not appeared $n$ times, where $n$ is a multiple of 3 .
Squares and Square Roots and Cubes and Cube Roots
Solution: