√164 =
2√41
≈ 12.806248
Square root of 164 — 12.806248 (2√41)
Irrational
The square root of 164 is about 12.806248, or exactly 2√41. It lies between 12 and 13.
- As a decimal
- ≈ 12.806248
- Simplified surd
- √164 = 2√41
- Between
- 12 < √164 < 13
- Squared
- 164² = 26896
- Cube root
- ∛164 ≈ 5.473704
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.
√164 = √(4 × 41) = 2√41
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 164?
About 12.806248, or exactly 2√41.
Q. Can the surd be simplified?
Yes: 164 = 4 × 41, so 2 comes out and it becomes 2√41.
Q. Between which integers does it fall?
Between 12 and 13.
Q. What is the cube root of 164?
About 5.473704.