Square root of 39
√39 ≈ 6.245. The square root of 39 is about 6.245. 39 is not a perfect square, so √39 is irrational: its decimals never end or repeat.
| Value | 6.244998 |
|---|---|
| Rounded | 6.2 (1 dp) · 6.24 (2 dp) · 6.245 (3 dp) |
| Simplest radical form | √39 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 39 squared | 1,521 |
Estimating √39 in your head
Start from the nearest perfect square, 6² = 36. 39 is 3 more than that. Divide the difference by twice the root, 12, and add it:
√39 ≈ 6 + 3 ÷ 12 ≈ 6.25
The true value is 6.245, so the one-step estimate is off by about 0.005. The estimate always comes out slightly high, and it is closest when 39 is near a perfect square. The method is explained in estimating square roots in your head.
Can √39 be simplified?
No. 39 has no perfect-square factor besides 1, so √39 is already in simplest radical form.
Frequently asked questions
What is the square root of 39?
The square root of 39 is about 6.245. 39 is not a perfect square, so √39 is irrational: its decimals never end or repeat.
Is 39 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √39 in simplest radical form?
√39 is already in simplest form: 39 has no square factor other than 1.
Practise estimating square rootsNearby: √38 · √40 · all square roots to 150