Square root of 15
√15 ≈ 3.873. The square root of 15 is about 3.873. 15 is not a perfect square, so √15 is irrational: its decimals never end or repeat.
| Value | 3.87298335 |
|---|---|
| Rounded | 3.9 (1 dp) · 3.87 (2 dp) · 3.873 (3 dp) |
| Simplest radical form | √15 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 15 squared | 225 |
Estimating √15 in your head
Start from the nearest perfect square, 4² = 16. 15 is 1 less than that. Divide the difference by twice the root, 8, and subtract it:
√15 ≈ 4 − 1 ÷ 8 ≈ 3.875
The true value is 3.873, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 15 is near a perfect square. The method is explained in estimating square roots in your head.
Can √15 be simplified?
No. 15 has no perfect-square factor besides 1, so √15 is already in simplest radical form.
Frequently asked questions
What is the square root of 15?
The square root of 15 is about 3.873. 15 is not a perfect square, so √15 is irrational: its decimals never end or repeat.
Is 15 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √15 in simplest radical form?
√15 is already in simplest form: 15 has no square factor other than 1.
Practise estimating square rootsNearby: √14 · √16 · all square roots to 150