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) ⇒ 5400=23 × 33 × 52 (B) On prime factorization of 5400 , we get 5400= 2 × 2 × 2 × 5 × 5 × 3 × 3 × 3. (C) ∴ 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 . (A) BACD (B) BADC (C) BDAC (D) ABDC

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) $∴ 5400$ 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 .

204 125 Squares and Square Roots and Cubes and Cube Roots Report Error

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