Square root of 21
√21 ≈ 4.5826. The square root of 21 is about 4.5826. 21 is not a perfect square, so √21 is irrational: its decimals never end or repeat.
| Value | 4.58257569 |
|---|---|
| Rounded | 4.6 (1 dp) · 4.58 (2 dp) · 4.583 (3 dp) |
| Simplest radical form | √21 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 21 squared | 441 |
Estimating √21 in your head
Start from the nearest perfect square, 5² = 25. 21 is 4 less than that. Divide the difference by twice the root, 10, and subtract it:
√21 ≈ 5 − 4 ÷ 10 ≈ 4.6
The true value is 4.5826, so the one-step estimate is off by about 0.017. The estimate always comes out slightly high, and it is closest when 21 is near a perfect square. The method is explained in estimating square roots in your head.
Can √21 be simplified?
No. 21 has no perfect-square factor besides 1, so √21 is already in simplest radical form.
Frequently asked questions
What is the square root of 21?
The square root of 21 is about 4.5826. 21 is not a perfect square, so √21 is irrational: its decimals never end or repeat.
Is 21 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √21 in simplest radical form?
√21 is already in simplest form: 21 has no square factor other than 1.
Practise estimating square rootsNearby: √20 · √22 · all square roots to 150