Square root of 110
√110 ≈ 10.4881. The square root of 110 is about 10.4881. 110 is not a perfect square, so √110 is irrational: its decimals never end or repeat.
| Value | 10.48808848 |
|---|---|
| Rounded | 10.5 (1 dp) · 10.49 (2 dp) · 10.488 (3 dp) |
| Simplest radical form | √110 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 110 squared | 12,100 |
Estimating √110 in your head
Start from the nearest perfect square, 10² = 100. 110 is 10 more than that. Divide the difference by twice the root, 20, and add it:
√110 ≈ 10 + 10 ÷ 20 ≈ 10.5
The true value is 10.4881, so the one-step estimate is off by about 0.012. The estimate always comes out slightly high, and it is closest when 110 is near a perfect square. The method is explained in estimating square roots in your head.
Can √110 be simplified?
No. 110 has no perfect-square factor besides 1, so √110 is already in simplest radical form.
Frequently asked questions
What is the square root of 110?
The square root of 110 is about 10.4881. 110 is not a perfect square, so √110 is irrational: its decimals never end or repeat.
Is 110 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √110 in simplest radical form?
√110 is already in simplest form: 110 has no square factor other than 1.
Practise estimating square rootsNearby: √109 · √111 · all square roots to 150