Square root of 23
√23 ≈ 4.7958. The square root of 23 is about 4.7958. 23 is not a perfect square, so √23 is irrational: its decimals never end or repeat.
| Value | 4.79583152 |
|---|---|
| Rounded | 4.8 (1 dp) · 4.80 (2 dp) · 4.796 (3 dp) |
| Simplest radical form | √23 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 23 squared | 529 |
Estimating √23 in your head
Start from the nearest perfect square, 5² = 25. 23 is 2 less than that. Divide the difference by twice the root, 10, and subtract it:
√23 ≈ 5 − 2 ÷ 10 ≈ 4.8
The true value is 4.7958, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 23 is near a perfect square. The method is explained in estimating square roots in your head.
Can √23 be simplified?
No. 23 has no perfect-square factor besides 1, so √23 is already in simplest radical form.
Frequently asked questions
What is the square root of 23?
The square root of 23 is about 4.7958. 23 is not a perfect square, so √23 is irrational: its decimals never end or repeat.
Is 23 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √23 in simplest radical form?
√23 is already in simplest form: 23 has no square factor other than 1.
Practise estimating square rootsNearby: √22 · √24 · all square roots to 150