Square root of 109
√109 ≈ 10.4403. The square root of 109 is about 10.4403. 109 is not a perfect square, so √109 is irrational: its decimals never end or repeat.
| Value | 10.44030651 |
|---|---|
| Rounded | 10.4 (1 dp) · 10.44 (2 dp) · 10.440 (3 dp) |
| Simplest radical form | √109 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 109 squared | 11,881 |
Estimating √109 in your head
Start from the nearest perfect square, 10² = 100. 109 is 9 more than that. Divide the difference by twice the root, 20, and add it:
√109 ≈ 10 + 9 ÷ 20 ≈ 10.45
The true value is 10.4403, so the one-step estimate is off by about 0.01. The estimate always comes out slightly high, and it is closest when 109 is near a perfect square. The method is explained in estimating square roots in your head.
Can √109 be simplified?
No. 109 has no perfect-square factor besides 1, so √109 is already in simplest radical form.
Frequently asked questions
What is the square root of 109?
The square root of 109 is about 10.4403. 109 is not a perfect square, so √109 is irrational: its decimals never end or repeat.
Is 109 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √109 in simplest radical form?
√109 is already in simplest form: 109 has no square factor other than 1.
Practise estimating square rootsNearby: √108 · √110 · all square roots to 150