√228 =
2√57
≈ 15.099669
Square root of 228 — 15.099669 (2√57)
Irrational
The square root of 228 is about 15.099669, or exactly 2√57. It lies between 15 and 16.
- As a decimal
- ≈ 15.099669
- Simplified surd
- √228 = 2√57
- Between
- 15 < √228 < 16
- Squared
- 228² = 51984
- Cube root
- ∛228 ≈ 6.109115
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.
√228 = √(4 × 57) = 2√57
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 228?
About 15.099669, or exactly 2√57.
Q. Can the surd be simplified?
Yes: 228 = 4 × 57, so 2 comes out and it becomes 2√57.
Q. Between which integers does it fall?
Between 15 and 16.
Q. What is the cube root of 228?
About 6.109115.