√176 =
4√11
≈ 13.266499
Square root of 176 — 13.266499 (4√11)
Irrational
The square root of 176 is about 13.266499, or exactly 4√11. It lies between 13 and 14.
- As a decimal
- ≈ 13.266499
- Simplified surd
- √176 = 4√11
- Between
- 13 < √176 < 14
- Squared
- 176² = 30976
- Cube root
- ∛176 ≈ 5.604079
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.
√176 = √(16 × 11) = 4√11
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 176?
About 13.266499, or exactly 4√11.
Q. Can the surd be simplified?
Yes: 176 = 16 × 11, so 4 comes out and it becomes 4√11.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 176?
About 5.604079.