Square root of 11
√11 ≈ 3.3166. The square root of 11 is about 3.3166. 11 is not a perfect square, so √11 is irrational: its decimals never end or repeat.
| Value | 3.31662479 |
|---|---|
| Rounded | 3.3 (1 dp) · 3.32 (2 dp) · 3.317 (3 dp) |
| Simplest radical form | √11 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 11 squared | 121 |
Estimating √11 in your head
Start from the nearest perfect square, 3² = 9. 11 is 2 more than that. Divide the difference by twice the root, 6, and add it:
√11 ≈ 3 + 2 ÷ 6 ≈ 3.333
The true value is 3.3166, so the one-step estimate is off by about 0.017. The estimate always comes out slightly high, and it is closest when 11 is near a perfect square. The method is explained in estimating square roots in your head.
Can √11 be simplified?
No. 11 has no perfect-square factor besides 1, so √11 is already in simplest radical form.
Frequently asked questions
What is the square root of 11?
The square root of 11 is about 3.3166. 11 is not a perfect square, so √11 is irrational: its decimals never end or repeat.
Is 11 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √11 in simplest radical form?
√11 is already in simplest form: 11 has no square factor other than 1.
Practise estimating square rootsNearby: √10 · √12 · all square roots to 150