√192 =
8√3
≈ 13.856406
Square root of 192 — 13.856406 (8√3)
Irrational
The square root of 192 is about 13.856406, or exactly 8√3. It lies between 13 and 14.
- As a decimal
- ≈ 13.856406
- Simplified surd
- √192 = 8√3
- Between
- 13 < √192 < 14
- Squared
- 192² = 36864
- Cube root
- ∛192 ≈ 5.768998
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.
√192 = √(64 × 3) = 8√3
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 192?
About 13.856406, or exactly 8√3.
Q. Can the surd be simplified?
Yes: 192 = 64 × 3, so 8 comes out and it becomes 8√3.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 192?
About 5.768998.