√175 =
5√7
≈ 13.228757
Square root of 175 — 13.228757 (5√7)
Irrational
The square root of 175 is about 13.228757, or exactly 5√7. It lies between 13 and 14.
- As a decimal
- ≈ 13.228757
- Simplified surd
- √175 = 5√7
- Between
- 13 < √175 < 14
- Squared
- 175² = 30625
- Cube root
- ∛175 ≈ 5.593445
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.
√175 = √(25 × 7) = 5√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 175?
About 13.228757, or exactly 5√7.
Q. Can the surd be simplified?
Yes: 175 = 25 × 7, so 5 comes out and it becomes 5√7.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 175?
About 5.593445.