Square root of 127
√127 ≈ 11.2694. The square root of 127 is about 11.2694. 127 is not a perfect square, so √127 is irrational: its decimals never end or repeat.
| Value | 11.26942767 |
|---|---|
| Rounded | 11.3 (1 dp) · 11.27 (2 dp) · 11.269 (3 dp) |
| Simplest radical form | √127 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 127 squared | 16,129 |
Estimating √127 in your head
Start from the nearest perfect square, 11² = 121. 127 is 6 more than that. Divide the difference by twice the root, 22, and add it:
√127 ≈ 11 + 6 ÷ 22 ≈ 11.273
The true value is 11.2694, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 127 is near a perfect square. The method is explained in estimating square roots in your head.
Can √127 be simplified?
No. 127 has no perfect-square factor besides 1, so √127 is already in simplest radical form.
Frequently asked questions
What is the square root of 127?
The square root of 127 is about 11.2694. 127 is not a perfect square, so √127 is irrational: its decimals never end or repeat.
Is 127 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √127 in simplest radical form?
√127 is already in simplest form: 127 has no square factor other than 1.
Practise estimating square rootsNearby: √126 · √128 · all square roots to 150