Square root of 114
√114 ≈ 10.6771. The square root of 114 is about 10.6771. 114 is not a perfect square, so √114 is irrational: its decimals never end or repeat.
| Value | 10.67707825 |
|---|---|
| Rounded | 10.7 (1 dp) · 10.68 (2 dp) · 10.677 (3 dp) |
| Simplest radical form | √114 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 114 squared | 12,996 |
Estimating √114 in your head
Start from the nearest perfect square, 11² = 121. 114 is 7 less than that. Divide the difference by twice the root, 22, and subtract it:
√114 ≈ 11 − 7 ÷ 22 ≈ 10.682
The true value is 10.6771, so the one-step estimate is off by about 0.005. The estimate always comes out slightly high, and it is closest when 114 is near a perfect square. The method is explained in estimating square roots in your head.
Can √114 be simplified?
No. 114 has no perfect-square factor besides 1, so √114 is already in simplest radical form.
Frequently asked questions
What is the square root of 114?
The square root of 114 is about 10.6771. 114 is not a perfect square, so √114 is irrational: its decimals never end or repeat.
Is 114 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √114 in simplest radical form?
√114 is already in simplest form: 114 has no square factor other than 1.
Practise estimating square rootsNearby: √113 · √115 · all square roots to 150