√160 =
4√10
≈ 12.649111
Square root of 160 — 12.649111 (4√10)
Irrational
The square root of 160 is about 12.649111, or exactly 4√10. It lies between 12 and 13.
- As a decimal
- ≈ 12.649111
- Simplified surd
- √160 = 4√10
- Between
- 12 < √160 < 13
- Squared
- 160² = 25600
- Cube root
- ∛160 ≈ 5.428835
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.
√160 = √(16 × 10) = 4√10
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 160?
About 12.649111, or exactly 4√10.
Q. Can the surd be simplified?
Yes: 160 = 16 × 10, so 4 comes out and it becomes 4√10.
Q. Between which integers does it fall?
Between 12 and 13.
Q. What is the cube root of 160?
About 5.428835.