SME
Grade 9 Math · Problem type
Simplify a cube root
Use this for “Simplify ∛54.”
Diagram
∛54 = ∛(2 × 3 × 3 × 3).
Each three of equal factors comes out as one: 3. ∛54 = 3∛2.
This is an example. Type your own values to start a new problem.
3
n
=
k
3
r
Formulas
k
=
∛(largest
perfect
cube
factor
of
n
)
3 = ∛(largest perfect cube factor of 54)
r
=
n
k
3
2
=
54
3
3
Assumptions
•
∛(ab) = ∛a × ∛b, for any numbers.
•
Each three equal prime factors come out as one.
•
The cube root is simplest when no cube factor but 1 is left inside.
Step-by-step
WE KNOW
n = 54
FIND
number outside (k), number left inside (r)
Step 1 · Find number outside (k)
Use k = ∛(largest perfect cube factor of n)
Find the largest perfect cube that divides the number: each group of three of equal prime factors brings one out.
k
=
∛(largest
perfect
cube
factor
of
54)
54
=
2
×
3
3
54 = 27 × 2
∛27 = 3
k
=
3
Step 2 · Find number left inside (r)
Use r = n ÷ k³
What is left under the root: divide out the perfect factor.
r
=
54
3
3
r
=
54
27
r
=
2
→
∛54
=
3∛2
Check
Put the numbers back in. Both sides should match.
3 = ∛(largest perfect cube factor of 54) ✓
2
=
54
3
3
✓
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