√198 =
3√22
≈ 14.071247
Square root of 198 — 14.071247 (3√22)
Irrational
The square root of 198 is about 14.071247, or exactly 3√22. It lies between 14 and 15.
- As a decimal
- ≈ 14.071247
- Simplified surd
- √198 = 3√22
- Between
- 14 < √198 < 15
- Squared
- 198² = 39204
- Cube root
- ∛198 ≈ 5.828477
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.
√198 = √(9 × 22) = 3√22
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 198?
About 14.071247, or exactly 3√22.
Q. Can the surd be simplified?
Yes: 198 = 9 × 22, so 3 comes out and it becomes 3√22.
Q. Between which integers does it fall?
Between 14 and 15.
Q. What is the cube root of 198?
About 5.828477.