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Question

If K = 216, then find the value of ∛K + ∛(K2).

The correct answer is

42

Write K as a perfect cube: 216 = 6³.

∛K = ∛216 = 6

∛(K²) = (∛K)² = 6² = 36

∛K + ∛(K²) = 6 + 36
= 42

Check: K² = 46656 and 36³ = 46656, so ∛(K²) is indeed 36.

Hence, 42.

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Important Questions from Cubes & Cube Roots

  1. What is the simplified value of \(\dfrac{(0.25)^3 + (0.05)^3}{(0.5)^3 + (0.1)^3}\)?

  2. What is the simplified value of \(\dfrac{(0.05)^3 + (0.005)^3}{(0.25)^3 + (0.025)^3}\)?

  3. A gardener organizes plants into rows to create a square formation but discovers that 15 plants are not included. If the total number of plants is 3984, then what is the number of plants in each row?

  4. If \(x=3-3^{1/3}-3^{2/3}\), then what is \(x(x-3)(x-6)\) equal to?

  5. If $11 \rightarrow 1331, 12 \rightarrow 1728$, then $13 \rightarrow ?$
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