Square root of 111
√111 ≈ 10.5357. The square root of 111 is about 10.5357. 111 is not a perfect square, so √111 is irrational: its decimals never end or repeat.
| Value | 10.53565375 |
|---|---|
| Rounded | 10.5 (1 dp) · 10.54 (2 dp) · 10.536 (3 dp) |
| Simplest radical form | √111 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 111 squared | 12,321 |
Estimating √111 in your head
Start from the nearest perfect square, 11² = 121. 111 is 10 less than that. Divide the difference by twice the root, 22, and subtract it:
√111 ≈ 11 − 10 ÷ 22 ≈ 10.545
The true value is 10.5357, so the one-step estimate is off by about 0.01. The estimate always comes out slightly high, and it is closest when 111 is near a perfect square. The method is explained in estimating square roots in your head.
Can √111 be simplified?
No. 111 has no perfect-square factor besides 1, so √111 is already in simplest radical form.
Frequently asked questions
What is the square root of 111?
The square root of 111 is about 10.5357. 111 is not a perfect square, so √111 is irrational: its decimals never end or repeat.
Is 111 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √111 in simplest radical form?
√111 is already in simplest form: 111 has no square factor other than 1.
Practise estimating square rootsNearby: √110 · √112 · all square roots to 150