Square root of 122
√122 ≈ 11.0454. The square root of 122 is about 11.0454. 122 is not a perfect square, so √122 is irrational: its decimals never end or repeat.
| Value | 11.04536102 |
|---|---|
| Rounded | 11.0 (1 dp) · 11.05 (2 dp) · 11.045 (3 dp) |
| Simplest radical form | √122 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 122 squared | 14,884 |
Estimating √122 in your head
Start from the nearest perfect square, 11² = 121. 122 is 1 more than that. Divide the difference by twice the root, 22, and add it:
√122 ≈ 11 + 1 ÷ 22 ≈ 11.045
The true value is 11.0454, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 122 is near a perfect square. The method is explained in estimating square roots in your head.
Can √122 be simplified?
No. 122 has no perfect-square factor besides 1, so √122 is already in simplest radical form.
Frequently asked questions
What is the square root of 122?
The square root of 122 is about 11.0454. 122 is not a perfect square, so √122 is irrational: its decimals never end or repeat.
Is 122 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √122 in simplest radical form?
√122 is already in simplest form: 122 has no square factor other than 1.
Practise estimating square rootsNearby: √121 · √123 · all square roots to 150