√153 =
3√17
≈ 12.369317
Square root of 153 — 12.369317 (3√17)
Irrational
The square root of 153 is about 12.369317, or exactly 3√17. It lies between 12 and 13.
- As a decimal
- ≈ 12.369317
- Simplified surd
- √153 = 3√17
- Between
- 12 < √153 < 13
- Squared
- 153² = 23409
- Cube root
- ∛153 ≈ 5.348481
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.
√153 = √(9 × 17) = 3√17
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 153?
About 12.369317, or exactly 3√17.
Q. Can the surd be simplified?
Yes: 153 = 9 × 17, so 3 comes out and it becomes 3√17.
Q. Between which integers does it fall?
Between 12 and 13.
Q. What is the cube root of 153?
About 5.348481.