√60 =
2√15
≈ 7.745967
Square root of 60 — 7.745967 (2√15)
Irrational
The square root of 60 is about 7.745967, or exactly 2√15. It lies between 7 and 8.
- As a decimal
- ≈ 7.745967
- Simplified surd
- √60 = 2√15
- Between
- 7 < √60 < 8
- Squared
- 60² = 3600
- Cube root
- ∛60 ≈ 3.914868
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.
√60 = √(4 × 15) = 2√15
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 60?
About 7.745967, or exactly 2√15.
Q. Can the surd be simplified?
Yes: 60 = 4 × 15, so 2 comes out and it becomes 2√15.
Q. Between which integers does it fall?
Between 7 and 8.
Q. What is the cube root of 60?
About 3.914868.