Square root of 107
√107 ≈ 10.3441. The square root of 107 is about 10.3441. 107 is not a perfect square, so √107 is irrational: its decimals never end or repeat.
| Value | 10.34408043 |
|---|---|
| Rounded | 10.3 (1 dp) · 10.34 (2 dp) · 10.344 (3 dp) |
| Simplest radical form | √107 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 107 squared | 11,449 |
Estimating √107 in your head
Start from the nearest perfect square, 10² = 100. 107 is 7 more than that. Divide the difference by twice the root, 20, and add it:
√107 ≈ 10 + 7 ÷ 20 ≈ 10.35
The true value is 10.3441, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 107 is near a perfect square. The method is explained in estimating square roots in your head.
Can √107 be simplified?
No. 107 has no perfect-square factor besides 1, so √107 is already in simplest radical form.
Frequently asked questions
What is the square root of 107?
The square root of 107 is about 10.3441. 107 is not a perfect square, so √107 is irrational: its decimals never end or repeat.
Is 107 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √107 in simplest radical form?
√107 is already in simplest form: 107 has no square factor other than 1.
Practise estimating square rootsNearby: √106 · √108 · all square roots to 150