√152 =
2√38
≈ 12.328828
Square root of 152 — 12.328828 (2√38)
Irrational
The square root of 152 is about 12.328828, or exactly 2√38. It lies between 12 and 13.
- As a decimal
- ≈ 12.328828
- Simplified surd
- √152 = 2√38
- Between
- 12 < √152 < 13
- Squared
- 152² = 23104
- Cube root
- ∛152 ≈ 5.336803
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.
√152 = √(4 × 38) = 2√38
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 152?
About 12.328828, or exactly 2√38.
Q. Can the surd be simplified?
Yes: 152 = 4 × 38, so 2 comes out and it becomes 2√38.
Q. Between which integers does it fall?
Between 12 and 13.
Q. What is the cube root of 152?
About 5.336803.