Square root of 63
√63 ≈ 7.9373. The square root of 63 is about 7.9373, which simplifies to 3√7. 63 is not a perfect square, so √63 is irrational: its decimals never end or repeat.
| Value | 7.93725393 |
|---|---|
| Rounded | 7.9 (1 dp) · 7.94 (2 dp) · 7.937 (3 dp) |
| Simplest radical form | 3√7 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 63 squared | 3,969 |
Estimating √63 in your head
Start from the nearest perfect square, 8² = 64. 63 is 1 less than that. Divide the difference by twice the root, 16, and subtract it:
√63 ≈ 8 − 1 ÷ 16 ≈ 7.938
The true value is 7.9373, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 63 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √63
Find the largest perfect square that divides 63: it is 9, since 63 = 9 × 7. Take its root outside: √63 = √9 × √7 = 3√7.
Frequently asked questions
What is the square root of 63?
The square root of 63 is about 7.9373, which simplifies to 3√7. 63 is not a perfect square, so √63 is irrational: its decimals never end or repeat.
Is 63 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √63 in simplest radical form?
√63 = √(9 × 7) = 3√7.
Practise estimating square rootsNearby: √62 · √64 · all square roots to 150