Square root of 22
√22 ≈ 4.6904. The square root of 22 is about 4.6904. 22 is not a perfect square, so √22 is irrational: its decimals never end or repeat.
| Value | 4.69041576 |
|---|---|
| Rounded | 4.7 (1 dp) · 4.69 (2 dp) · 4.690 (3 dp) |
| Simplest radical form | √22 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 22 squared | 484 |
Estimating √22 in your head
Start from the nearest perfect square, 5² = 25. 22 is 3 less than that. Divide the difference by twice the root, 10, and subtract it:
√22 ≈ 5 − 3 ÷ 10 ≈ 4.7
The true value is 4.6904, so the one-step estimate is off by about 0.01. The estimate always comes out slightly high, and it is closest when 22 is near a perfect square. The method is explained in estimating square roots in your head.
Can √22 be simplified?
No. 22 has no perfect-square factor besides 1, so √22 is already in simplest radical form.
Frequently asked questions
What is the square root of 22?
The square root of 22 is about 4.6904. 22 is not a perfect square, so √22 is irrational: its decimals never end or repeat.
Is 22 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √22 in simplest radical form?
√22 is already in simplest form: 22 has no square factor other than 1.
Practise estimating square rootsNearby: √21 · √23 · all square roots to 150