Square root of 123
√123 ≈ 11.0905. The square root of 123 is about 11.0905. 123 is not a perfect square, so √123 is irrational: its decimals never end or repeat.
| Value | 11.09053651 |
|---|---|
| Rounded | 11.1 (1 dp) · 11.09 (2 dp) · 11.091 (3 dp) |
| Simplest radical form | √123 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 123 squared | 15,129 |
Estimating √123 in your head
Start from the nearest perfect square, 11² = 121. 123 is 2 more than that. Divide the difference by twice the root, 22, and add it:
√123 ≈ 11 + 2 ÷ 22 ≈ 11.091
The true value is 11.0905, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 123 is near a perfect square. The method is explained in estimating square roots in your head.
Can √123 be simplified?
No. 123 has no perfect-square factor besides 1, so √123 is already in simplest radical form.
Frequently asked questions
What is the square root of 123?
The square root of 123 is about 11.0905. 123 is not a perfect square, so √123 is irrational: its decimals never end or repeat.
Is 123 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √123 in simplest radical form?
√123 is already in simplest form: 123 has no square factor other than 1.
Practise estimating square rootsNearby: √122 · √124 · all square roots to 150