Square root of 14
√14 ≈ 3.7417. The square root of 14 is about 3.7417. 14 is not a perfect square, so √14 is irrational: its decimals never end or repeat.
| Value | 3.74165739 |
|---|---|
| Rounded | 3.7 (1 dp) · 3.74 (2 dp) · 3.742 (3 dp) |
| Simplest radical form | √14 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 14 squared | 196 |
Estimating √14 in your head
Start from the nearest perfect square, 4² = 16. 14 is 2 less than that. Divide the difference by twice the root, 8, and subtract it:
√14 ≈ 4 − 2 ÷ 8 ≈ 3.75
The true value is 3.7417, so the one-step estimate is off by about 0.008. The estimate always comes out slightly high, and it is closest when 14 is near a perfect square. The method is explained in estimating square roots in your head.
Can √14 be simplified?
No. 14 has no perfect-square factor besides 1, so √14 is already in simplest radical form.
Frequently asked questions
What is the square root of 14?
The square root of 14 is about 3.7417. 14 is not a perfect square, so √14 is irrational: its decimals never end or repeat.
Is 14 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √14 in simplest radical form?
√14 is already in simplest form: 14 has no square factor other than 1.
Practise estimating square rootsNearby: √13 · √15 · all square roots to 150