Square root of 13
√13 ≈ 3.6056. The square root of 13 is about 3.6056. 13 is not a perfect square, so √13 is irrational: its decimals never end or repeat.
| Value | 3.60555128 |
|---|---|
| Rounded | 3.6 (1 dp) · 3.61 (2 dp) · 3.606 (3 dp) |
| Simplest radical form | √13 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 13 squared | 169 |
Estimating √13 in your head
Start from the nearest perfect square, 4² = 16. 13 is 3 less than that. Divide the difference by twice the root, 8, and subtract it:
√13 ≈ 4 − 3 ÷ 8 ≈ 3.625
The true value is 3.6056, so the one-step estimate is off by about 0.019. The estimate always comes out slightly high, and it is closest when 13 is near a perfect square. The method is explained in estimating square roots in your head.
Can √13 be simplified?
No. 13 has no perfect-square factor besides 1, so √13 is already in simplest radical form.
Frequently asked questions
What is the square root of 13?
The square root of 13 is about 3.6056. 13 is not a perfect square, so √13 is irrational: its decimals never end or repeat.
Is 13 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √13 in simplest radical form?
√13 is already in simplest form: 13 has no square factor other than 1.
Practise estimating square rootsNearby: √12 · √14 · all square roots to 150