√75 =
5√3
≈ 8.660254
Square root of 75 — 8.660254 (5√3)
Irrational
The square root of 75 is about 8.660254, or exactly 5√3. It lies between 8 and 9.
- As a decimal
- ≈ 8.660254
- Simplified surd
- √75 = 5√3
- Between
- 8 < √75 < 9
- Squared
- 75² = 5625
- Cube root
- ∛75 ≈ 4.217163
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.
√75 = √(25 × 3) = 5√3
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 75?
About 8.660254, or exactly 5√3.
Q. Can the surd be simplified?
Yes: 75 = 25 × 3, so 5 comes out and it becomes 5√3.
Q. Between which integers does it fall?
Between 8 and 9.
Q. What is the cube root of 75?
About 4.217163.