Square root of 31
√31 ≈ 5.5678. The square root of 31 is about 5.5678. 31 is not a perfect square, so √31 is irrational: its decimals never end or repeat.
| Value | 5.56776436 |
|---|---|
| Rounded | 5.6 (1 dp) · 5.57 (2 dp) · 5.568 (3 dp) |
| Simplest radical form | √31 |
| Perfect square? | No — between 5² = 25 and 6² = 36 |
| 31 squared | 961 |
Estimating √31 in your head
Start from the nearest perfect square, 6² = 36. 31 is 5 less than that. Divide the difference by twice the root, 12, and subtract it:
√31 ≈ 6 − 5 ÷ 12 ≈ 5.583
The true value is 5.5678, so the one-step estimate is off by about 0.016. The estimate always comes out slightly high, and it is closest when 31 is near a perfect square. The method is explained in estimating square roots in your head.
Can √31 be simplified?
No. 31 has no perfect-square factor besides 1, so √31 is already in simplest radical form.
Frequently asked questions
What is the square root of 31?
The square root of 31 is about 5.5678. 31 is not a perfect square, so √31 is irrational: its decimals never end or repeat.
Is 31 a perfect square?
No. It lies between 5² = 25 and 6² = 36.
What is √31 in simplest radical form?
√31 is already in simplest form: 31 has no square factor other than 1.
Practise estimating square rootsNearby: √30 · √32 · all square roots to 150