Square root of 3
√3 ≈ 1.7321. The square root of 3 is about 1.7321. 3 is not a perfect square, so √3 is irrational: its decimals never end or repeat.
| Value | 1.73205081 |
|---|---|
| Rounded | 1.7 (1 dp) · 1.73 (2 dp) · 1.732 (3 dp) |
| Simplest radical form | √3 |
| Perfect square? | No — between 1² = 1 and 2² = 4 |
| 3 squared | 9 |
Estimating √3 in your head
Start from the nearest perfect square, 2² = 4. 3 is 1 less than that. Divide the difference by twice the root, 4, and subtract it:
√3 ≈ 2 − 1 ÷ 4 ≈ 1.75
The true value is 1.7321, so the one-step estimate is off by about 0.018. The estimate always comes out slightly high, and it is closest when 3 is near a perfect square. The method is explained in estimating square roots in your head.
Can √3 be simplified?
No. 3 has no perfect-square factor besides 1, so √3 is already in simplest radical form.
Frequently asked questions
What is the square root of 3?
The square root of 3 is about 1.7321. 3 is not a perfect square, so √3 is irrational: its decimals never end or repeat.
Is 3 a perfect square?
No. It lies between 1² = 1 and 2² = 4.
What is √3 in simplest radical form?
√3 is already in simplest form: 3 has no square factor other than 1.
Practise estimating square rootsNearby: √2 · √4 · all square roots to 150