Square root of 19
√19 ≈ 4.3589. The square root of 19 is about 4.3589. 19 is not a perfect square, so √19 is irrational: its decimals never end or repeat.
| Value | 4.35889894 |
|---|---|
| Rounded | 4.4 (1 dp) · 4.36 (2 dp) · 4.359 (3 dp) |
| Simplest radical form | √19 |
| Perfect square? | No — between 4² = 16 and 5² = 25 |
| 19 squared | 361 |
Estimating √19 in your head
Start from the nearest perfect square, 4² = 16. 19 is 3 more than that. Divide the difference by twice the root, 8, and add it:
√19 ≈ 4 + 3 ÷ 8 ≈ 4.375
The true value is 4.3589, so the one-step estimate is off by about 0.016. The estimate always comes out slightly high, and it is closest when 19 is near a perfect square. The method is explained in estimating square roots in your head.
Can √19 be simplified?
No. 19 has no perfect-square factor besides 1, so √19 is already in simplest radical form.
Frequently asked questions
What is the square root of 19?
The square root of 19 is about 4.3589. 19 is not a perfect square, so √19 is irrational: its decimals never end or repeat.
Is 19 a perfect square?
No. It lies between 4² = 16 and 5² = 25.
What is √19 in simplest radical form?
√19 is already in simplest form: 19 has no square factor other than 1.
Practise estimating square rootsNearby: √18 · √20 · all square roots to 150