√150 =
5√6
≈ 12.247449
Square root of 150 — 12.247449 (5√6)
Irrational
The square root of 150 is about 12.247449, or exactly 5√6. It lies between 12 and 13.
- As a decimal
- ≈ 12.247449
- Simplified surd
- √150 = 5√6
- Between
- 12 < √150 < 13
- Squared
- 150² = 22500
- Cube root
- ∛150 ≈ 5.313293
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.
√150 = √(25 × 6) = 5√6
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 150?
About 12.247449, or exactly 5√6.
Q. Can the surd be simplified?
Yes: 150 = 25 × 6, so 5 comes out and it becomes 5√6.
Q. Between which integers does it fall?
Between 12 and 13.
Q. What is the cube root of 150?
About 5.313293.