√224 =
4√14
≈ 14.96663
Square root of 224 — 14.96663 (4√14)
Irrational
The square root of 224 is about 14.96663, or exactly 4√14. It lies between 14 and 15.
- As a decimal
- ≈ 14.96663
- Simplified surd
- √224 = 4√14
- Between
- 14 < √224 < 15
- Squared
- 224² = 50176
- Cube root
- ∛224 ≈ 6.073178
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.
√224 = √(16 × 14) = 4√14
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 224?
About 14.96663, or exactly 4√14.
Q. Can the surd be simplified?
Yes: 224 = 16 × 14, so 4 comes out and it becomes 4√14.
Q. Between which integers does it fall?
Between 14 and 15.
Q. What is the cube root of 224?
About 6.073178.