√180 =
6√5
≈ 13.416408
Square root of 180 — 13.416408 (6√5)
Irrational
The square root of 180 is about 13.416408, or exactly 6√5. It lies between 13 and 14.
- As a decimal
- ≈ 13.416408
- Simplified surd
- √180 = 6√5
- Between
- 13 < √180 < 14
- Squared
- 180² = 32400
- Cube root
- ∛180 ≈ 5.646216
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.
√180 = √(36 × 5) = 6√5
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 180?
About 13.416408, or exactly 6√5.
Q. Can the surd be simplified?
Yes: 180 = 36 × 5, so 6 comes out and it becomes 6√5.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 180?
About 5.646216.