√50 =
5√2
≈ 7.071068
Square root of 50 — 7.071068 (5√2)
Irrational
The square root of 50 is about 7.071068, or exactly 5√2. It lies between 7 and 8.
- As a decimal
- ≈ 7.071068
- Simplified surd
- √50 = 5√2
- Between
- 7 < √50 < 8
- Squared
- 50² = 2500
- Cube root
- ∛50 ≈ 3.684031
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.
√50 = √(25 × 2) = 5√2
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 50?
About 7.071068, or exactly 5√2.
Q. Can the surd be simplified?
Yes: 50 = 25 × 2, so 5 comes out and it becomes 5√2.
Q. Between which integers does it fall?
Between 7 and 8.
Q. What is the cube root of 50?
About 3.684031.