Square root of 2
√2 ≈ 1.4142. The square root of 2 is about 1.4142. 2 is not a perfect square, so √2 is irrational: its decimals never end or repeat.
| Value | 1.41421356 |
|---|---|
| Rounded | 1.4 (1 dp) · 1.41 (2 dp) · 1.414 (3 dp) |
| Simplest radical form | √2 |
| Perfect square? | No — between 1² = 1 and 2² = 4 |
| 2 squared | 4 |
Estimating √2 in your head
Start from the nearest perfect square, 1² = 1. 2 is 1 more than that. Divide the difference by twice the root, 2, and add it:
√2 ≈ 1 + 1 ÷ 2 ≈ 1.5
The true value is 1.4142, so the one-step estimate is off by about 0.086. The estimate always comes out slightly high, and it is closest when 2 is near a perfect square. The method is explained in estimating square roots in your head.
Can √2 be simplified?
No. 2 has no perfect-square factor besides 1, so √2 is already in simplest radical form.
Frequently asked questions
What is the square root of 2?
The square root of 2 is about 1.4142. 2 is not a perfect square, so √2 is irrational: its decimals never end or repeat.
Is 2 a perfect square?
No. It lies between 1² = 1 and 2² = 4.
What is √2 in simplest radical form?
√2 is already in simplest form: 2 has no square factor other than 1.
Practise estimating square rootsNearby: √3 · all square roots to 150