√172 =
2√43
≈ 13.114877
Square root of 172 — 13.114877 (2√43)
Irrational
The square root of 172 is about 13.114877, or exactly 2√43. It lies between 13 and 14.
- As a decimal
- ≈ 13.114877
- Simplified surd
- √172 = 2√43
- Between
- 13 < √172 < 14
- Squared
- 172² = 29584
- Cube root
- ∛172 ≈ 5.561298
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.
√172 = √(4 × 43) = 2√43
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 172?
About 13.114877, or exactly 2√43.
Q. Can the surd be simplified?
Yes: 172 = 4 × 43, so 2 comes out and it becomes 2√43.
Q. Between which integers does it fall?
Between 13 and 14.
Q. What is the cube root of 172?
About 5.561298.