What Is A Cube Root?
The cube root of a number $n$ is the value $r$ that satisfies $r^3 = n$. So $\sqrt[3]{1080}$ is the number you multiply by itself three times to land on $1080$.
No whole number does this, because $10^3 = 1000$ (too small) and $11^3 = 1331$ (too big). That places $\sqrt[3]{1080}$ between $10$ and $11$, close to $10.26$. Written with a rational exponent, the same value is $(1080)^{1/3}$.
Where ∛1080 Shows Up
The cube root answers a volume question: a cube holding $1080$ cubic units has an edge of $\sqrt[3]{1080} \approx 10.26$ units. Because $1080 = 6^3 \times 5$, that edge is exactly $6$ times the edge of a unit-5 cube, which is what the simplified form $6\sqrt[3]{5}$ records. The same number shows up when a recipe, tank, or 3D model is scaled so its volume grows by a factor of $1080$: every length scales by $\sqrt[3]{1080}$.
Quick Reference Table
Number $n$ | $\sqrt[3]{n}$ | Simplified | Perfect Cube? |
|---|---|---|---|
27 | 3 | 3 | Yes |
64 | 4 | 4 | Yes |
125 | 5 | 5 | Yes |
135 | $\approx 5.130$ | $3\sqrt[3]{5}$ | No |
216 | 6 | 6 | Yes |
540 | $\approx 8.143$ | $3\sqrt[3]{20}$ | No |
1080 | $\approx 10.260$ | $6\sqrt[3]{5}$ | No |
1000 | 10 | 10 | Yes |
1728 | 12 | 12 | Yes |
How Do You Simplify The Cube Root Of 1080?
The cleanest route is prime factorization: break $1080$ into primes, then pull out any factor that appears three times.
Step 1: Factor $1080$ into primes.
$1080 = 2 \times 540$
$= 2 \times 2 \times 270$
$= 2 \times 2 \times 2 \times 135$
$= 2^3 \times 3^3 \times 5$
Step 2: Group the triples. Both $2^3$ and $3^3$ are complete triples; the $5$ is alone.
$1080 = (2 \times 3)^3 \times 5 = 6^3 \times 5$
Step 3: A complete cube leaves the radical as its base.
$\sqrt[3]{1080} = \sqrt[3]{6^3 \times 5} = 6\sqrt[3]{5}$
Step 4: Approximate the leftover. Since $\sqrt[3]{5} \approx 1.7100$:
$6 \times 1.7100 = 10.2599$
Final answer: $\sqrt[3]{1080} = 6\sqrt[3]{5} \approx 10.26$.
Is The Cube Root Of 1080 Rational Or Irrational?
$\sqrt[3]{1080}$ is irrational. Its value cannot be written as a fraction of two integers, and its decimal expansion neither ends nor repeats.
The reason sits in the factor that survives simplification. A whole number has a rational cube root only when every prime in its factorization appears a multiple of three times, making it a perfect cube. In $1080 = 2^3 \times 3^3 \times 5$, the prime $5$ appears once, not a multiple of three, so $1080$ is not a perfect cube. That leftover $5$ locks $\sqrt[3]{5}$ inside the answer, and $\sqrt[3]{5}$ is itself an irrational number. A whole number times an irrational stays irrational, so $6\sqrt[3]{5}$ is irrational too.
If you want the underlying rule for the cube-root operation, Wolfram MathWorld's entry on the cube root states it precisely.
Examples Of The Cube Root Of 1080
Example 1
Confirm the simplified form is correct.
Cube $6\sqrt[3]{5}$ and check it returns $1080$.
$(6\sqrt[3]{5})^3 = 6^3 \times (\sqrt[3]{5})^3$
$= 216 \times 5$
$= 1080$
The simplified radical is exact.
Example 2 (Wrong path first)
Simplify $\sqrt[3]{1080}$ by pulling out a square factor.
Wrong attempt. A student notices $1080 = 36 \times 30$ and writes $\sqrt[3]{1080} = 6\sqrt[3]{30}$, treating the $\sqrt[3]{36} = 6$ the way a square root would.
The break. Check it: $(6\sqrt[3]{30})^3 = 216 \times 30 = 6480$, not $1080$. The result is wrong because cube roots pull out cubes, not squares. $36$ is a perfect square, not a perfect cube.
Correct. Factor to primes and remove a complete triple: $1080 = 6^3 \times 5$, so $\sqrt[3]{1080} = 6\sqrt[3]{5}$, and $(6\sqrt[3]{5})^3 = 1080$.
Example 3
Evaluate $\sqrt[3]{1080}$ to two decimal places without simplifying.
$10^3 = 1000$ and $10.3^3 = 1092.727$
Since $1080$ sits just below $1092.727$, try $10.26$:
$10.26^3 = 1080.045$
So $\sqrt[3]{1080} \approx 10.26$.
Example 4
Simplify $\sqrt[3]{\dfrac{1080}{125}}$.
Split the radical over the fraction.
$\sqrt[3]{\dfrac{1080}{125}} = \dfrac{\sqrt[3]{1080}}{\sqrt[3]{125}}$
$= \dfrac{6\sqrt[3]{5}}{5}$
The denominator is a perfect cube, so it simplifies cleanly to $5$.
Example 5
A storage cube holds 1080 litres. What is its edge length in decimetres (1 litre = 1 cubic decimetre)?
Edge $= \sqrt[3]{1080}$ dm
$= 6\sqrt[3]{5} \approx 10.26$ dm
The cube is about $10.26$ dm, or just over a metre, on each side.
Common Mistakes
Mistake 1: Treating 1080 as a perfect cube
Where it slips in: Rushing to write $\sqrt[3]{1080}$ as a whole number.
Don't do this: Rounding $10.26$ to $10$ and reporting $\sqrt[3]{1080} = 10$.
The correct way: Check the neighbours first. $10^3 = 1000$ and $11^3 = 1331$; $1080$ is neither, so the answer is the irrational $6\sqrt[3]{5}$, not a clean integer. Students who verify a method before reaching for the calculator catch this every time, because the cube-check makes the gap between $1000$ and $1080$ visible.
Mistake 2: Pulling out non-cube factors
Where it slips in: Copying square-root simplification habits onto a cube root.
Don't do this: Removing $\sqrt[3]{36} = 6$ from $\sqrt[3]{1080}$ to get $6\sqrt[3]{30}$.
The correct way: For a cube root, only a factor appearing three times comes out. Factor to primes, group in threes: $1080 = 2^3 \times 3^3 \times 5$ gives $6\sqrt[3]{5}$.
Mistake 3: Losing the leftover factor
Where it slips in: Simplifying $6^3 \times 5$ and forgetting the $5$.
Don't do this: Writing $\sqrt[3]{1080} = 6$.
The correct way: The stray $5$ stays under the radical: $\sqrt[3]{1080} = 6\sqrt[3]{5}$. Only the complete cube $6^3$ leaves.
Conclusion
The cube root of 1080 is $6\sqrt[3]{5}$, close to $10.26$, and it stays irrational because the lone factor of $5$ never forms a complete cube. Keep the radical form for exact algebra and switch to the decimal only when a problem needs a number. To build this skill with a teacher, explore Bhanzu's algebra tutor sessions, get targeted help with algebra, or join live math classes online.
Want a live Bhanzu trainer to walk through more cube root problems? Book a free demo class.
Read More
Cube Root of 36 — another non-perfect cube that cannot be simplified at all.
Cube Root of 64 — a clean perfect cube for comparison.
Cube Root of 343 — how a perfect cube of an odd number behaves.
Simplifying Radical Expressions — the general method behind pulling factors out of any root.
Square Root Tricks — fast estimation methods that transfer to cube roots.
Square Root 1 to 25 — the companion reference table for square roots.
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