√189 =
3√21
≈ 13.747727
Square root of 189 — 13.747727 (3√21)
Irrational
The square root of 189 is about 13.747727, or exactly 3√21. It lies between 13 and 14.
- As a decimal
- ≈ 13.747727
- Simplified surd
- √189 = 3√21
- Between
- 13 < √189 < 14
- Squared
- 189² = 35721
- Cube root
- ∛189 ≈ 5.738794
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.
√189 = √(9 × 21) = 3√21
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 189?
About 13.747727, or exactly 3√21.
Q. Can the surd be simplified?
Yes: 189 = 9 × 21, so 3 comes out and it becomes 3√21.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 189?
About 5.738794.