√112 =
4√7
≈ 10.583005
Square root of 112 — 10.583005 (4√7)
Irrational
The square root of 112 is about 10.583005, or exactly 4√7. It lies between 10 and 11.
- As a decimal
- ≈ 10.583005
- Simplified surd
- √112 = 4√7
- Between
- 10 < √112 < 11
- Squared
- 112² = 12544
- Cube root
- ∛112 ≈ 4.820285
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.
√112 = √(16 × 7) = 4√7
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 112?
About 10.583005, or exactly 4√7.
Q. Can the surd be simplified?
Yes: 112 = 16 × 7, so 4 comes out and it becomes 4√7.
Q. Between which integers does it fall?
Between 10 and 11.
Q. What is the cube root of 112?
About 4.820285.