Square root of 124
√124 ≈ 11.1355. The square root of 124 is about 11.1355, which simplifies to 2√31. 124 is not a perfect square, so √124 is irrational: its decimals never end or repeat.
| Value | 11.13552873 |
|---|---|
| Rounded | 11.1 (1 dp) · 11.14 (2 dp) · 11.136 (3 dp) |
| Simplest radical form | 2√31 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 124 squared | 15,376 |
Estimating √124 in your head
Start from the nearest perfect square, 11² = 121. 124 is 3 more than that. Divide the difference by twice the root, 22, and add it:
√124 ≈ 11 + 3 ÷ 22 ≈ 11.136
The true value is 11.1355, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 124 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √124
Find the largest perfect square that divides 124: it is 4, since 124 = 4 × 31. Take its root outside: √124 = √4 × √31 = 2√31.
Frequently asked questions
What is the square root of 124?
The square root of 124 is about 11.1355, which simplifies to 2√31. 124 is not a perfect square, so √124 is irrational: its decimals never end or repeat.
Is 124 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √124 in simplest radical form?
√124 = √(4 × 31) = 2√31.
Practise estimating square rootsNearby: √123 · √125 · all square roots to 150