Square root of 37
√37 ≈ 6.0828. The square root of 37 is about 6.0828. 37 is not a perfect square, so √37 is irrational: its decimals never end or repeat.
| Value | 6.08276253 |
|---|---|
| Rounded | 6.1 (1 dp) · 6.08 (2 dp) · 6.083 (3 dp) |
| Simplest radical form | √37 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 37 squared | 1,369 |
Estimating √37 in your head
Start from the nearest perfect square, 6² = 36. 37 is 1 more than that. Divide the difference by twice the root, 12, and add it:
√37 ≈ 6 + 1 ÷ 12 ≈ 6.083
The true value is 6.0828, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 37 is near a perfect square. The method is explained in estimating square roots in your head.
Can √37 be simplified?
No. 37 has no perfect-square factor besides 1, so √37 is already in simplest radical form.
Frequently asked questions
What is the square root of 37?
The square root of 37 is about 6.0828. 37 is not a perfect square, so √37 is irrational: its decimals never end or repeat.
Is 37 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √37 in simplest radical form?
√37 is already in simplest form: 37 has no square factor other than 1.
Practise estimating square rootsNearby: √36 · √38 · all square roots to 150