Meera made this factor tree for 1350. What is the smallest number she must multiply 1350 by so that the product is a perfect cube?

Class 8Cubes and Cube RootsCubes and Roots

Step-by-Step Solution

1350 = 2 \times 3^{3} \times 5^{2}

. To complete groups of three we need two more 2s and one more 5:

2^{2} \times 5 = 20

. Check:

1350 \times 20 = 27000 = 3 0^{3}

Answer: A) 20

Key idea: Cube root by prime factorisation

**Step 1**: factorise into primes.
**Step 2**: group the prime factors into TRIPLES (three of the same).
**Step 3**: take ONE factor from each triple — their product is the cube root.

Example: ∛216.

216 = 2^{3} \times 3^{3} = (2 \times 3)^{3} = 6^{3}

. So ∛216 = 6.

Example: ∛13824.

13824 = 2^{9} \times 3^{3} = (2^{3} \times 3)^{3} = (8 \times 3)^{3} = 2 4^{3}

. So ∛13824 = 24.

If any prime doesn't form a complete triple, the number isn't a perfect cube.

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