√54 =
3√6
≈ 7.348469
Square root of 54 — 7.348469 (3√6)
Irrational
The square root of 54 is about 7.348469, or exactly 3√6. It lies between 7 and 8.
- As a decimal
- ≈ 7.348469
- Simplified surd
- √54 = 3√6
- Between
- 7 < √54 < 8
- Squared
- 54² = 2916
- Cube root
- ∛54 ≈ 3.779763
How the surd is simplified
Pull out the largest square factor. Since 50 = 25 × 2, the root of 25 comes out as 5 and the 2 stays behind: 5√2.
√54 = √(9 × 6) = 3√6
Nearby numbers
From 1 to 200
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How to read this
- The decimal is rounded; the surd form is the exact value.
- Pulling out a square factor simplifies the surd — √50 = 5√2.
- If the number is not a perfect square, the decimal never ends (irrational).
- Knowing which two integers it sits between is enough to estimate in your head.
Frequently asked questions
Q. What is the square root of 54?
About 7.348469, or exactly 3√6.
Q. Can the surd be simplified?
Yes: 54 = 9 × 6, so 3 comes out and it becomes 3√6.
Q. Between which integers does it fall?
Between 7 and 8.
Q. What is the cube root of 54?
About 3.779763.