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Simplifying cube roots worksheets

Simplifying a cube root means finding a perfect cube hidden inside the number. These free printable worksheets give ten a page, such as ∛135, which is 27 × 5 and so comes out as 3∛5. The answer key shows the split that produced each one.

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Simplifying cube roots
Simplifying cube roots worksheet — Cubes 8, 27 and 64, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

There are only three cubes to look for on this sheet: 8, 27 and 64. A student who knows them tries each one, and if it divides, that factor comes out as its cube root. ∛320 is ∛(64 × 5), and that is 4∛5. The biggest cube that divides is the one to use, because ∛320 = 2∛40 is a true sentence and it is not finished yet.

Why this sheet works

Students coming straight from square roots tend to stop in the wrong place. ∛324 is 3∛12, and it feels unfinished because 12 has a 4 in it, and 4 is a perfect square. That does not matter here. The test for a cube root is whether anything left inside is a perfect cube, and 12 has no factor of 8 or 27, so 3∛12 is the answer. In the same way, ∛243 is 3∛9, with a 9 left under the sign.

How this one works

∛135

135 = 27 × 5
∛135 = ∛27 × ∛5
∛135 = 3∛5
  1. Split 135 into a perfect cube times whatever is left: 135 = 27 × 5. 27 is 3 cubed, and 5 has no cube factor of its own — that last part is what makes this the LARGEST perfect cube inside, and it is where the answer stops.
  2. A root splits across a product, so the one root becomes two.
  3. ∛27 is 3, so it comes out in front. ∛5 stays under the sign, because 5 has nothing more to give.

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