Square root of 126
√126 ≈ 11.225. The square root of 126 is about 11.225, which simplifies to 3√14. 126 is not a perfect square, so √126 is irrational: its decimals never end or repeat.
| Value | 11.22497216 |
|---|---|
| Rounded | 11.2 (1 dp) · 11.22 (2 dp) · 11.225 (3 dp) |
| Simplest radical form | 3√14 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 126 squared | 15,876 |
Estimating √126 in your head
Start from the nearest perfect square, 11² = 121. 126 is 5 more than that. Divide the difference by twice the root, 22, and add it:
√126 ≈ 11 + 5 ÷ 22 ≈ 11.227
The true value is 11.225, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 126 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √126
Find the largest perfect square that divides 126: it is 9, since 126 = 9 × 14. Take its root outside: √126 = √9 × √14 = 3√14.
Frequently asked questions
What is the square root of 126?
The square root of 126 is about 11.225, which simplifies to 3√14. 126 is not a perfect square, so √126 is irrational: its decimals never end or repeat.
Is 126 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √126 in simplest radical form?
√126 = √(9 × 14) = 3√14.
Practise estimating square rootsNearby: √125 · √127 · all square roots to 150