√63 =
3√7
≈ 7.937254
Square root of 63 — 7.937254 (3√7)
Irrational
The square root of 63 is about 7.937254, or exactly 3√7. It lies between 7 and 8.
- As a decimal
- ≈ 7.937254
- Simplified surd
- √63 = 3√7
- Between
- 7 < √63 < 8
- Squared
- 63² = 3969
- Cube root
- ∛63 ≈ 3.979057
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.
√63 = √(9 × 7) = 3√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 63?
About 7.937254, or exactly 3√7.
Q. Can the surd be simplified?
Yes: 63 = 9 × 7, so 3 comes out and it becomes 3√7.
Q. Between which integers does it fall?
Between 7 and 8.
Q. What is the cube root of 63?
About 3.979057.