√212 =
2√53
≈ 14.56022
Square root of 212 — 14.56022 (2√53)
Irrational
The square root of 212 is about 14.56022, or exactly 2√53. It lies between 14 and 15.
- As a decimal
- ≈ 14.56022
- Simplified surd
- √212 = 2√53
- Between
- 14 < √212 < 15
- Squared
- 212² = 44944
- Cube root
- ∛212 ≈ 5.962732
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.
√212 = √(4 × 53) = 2√53
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 212?
About 14.56022, or exactly 2√53.
Q. Can the surd be simplified?
Yes: 212 = 4 × 53, so 2 comes out and it becomes 2√53.
Q. Between which integers does it fall?
Between 14 and 15.
Q. What is the cube root of 212?
About 5.962732.