Square root of 6
√6 ≈ 2.4495. The square root of 6 is about 2.4495. 6 is not a perfect square, so √6 is irrational: its decimals never end or repeat.
| Value | 2.44948974 |
|---|---|
| Rounded | 2.4 (1 dp) · 2.45 (2 dp) · 2.449 (3 dp) |
| Simplest radical form | √6 |
| Perfect square? | No — between 2² = 4 and 3² = 9 |
| 6 squared | 36 |
Estimating √6 in your head
Start from the nearest perfect square, 2² = 4. 6 is 2 more than that. Divide the difference by twice the root, 4, and add it:
√6 ≈ 2 + 2 ÷ 4 ≈ 2.5
The true value is 2.4495, so the one-step estimate is off by about 0.051. The estimate always comes out slightly high, and it is closest when 6 is near a perfect square. The method is explained in estimating square roots in your head.
Can √6 be simplified?
No. 6 has no perfect-square factor besides 1, so √6 is already in simplest radical form.
Frequently asked questions
What is the square root of 6?
The square root of 6 is about 2.4495. 6 is not a perfect square, so √6 is irrational: its decimals never end or repeat.
Is 6 a perfect square?
No. It lies between 2² = 4 and 3² = 9.
What is √6 in simplest radical form?
√6 is already in simplest form: 6 has no square factor other than 1.
Practise estimating square rootsNearby: √5 · √7 · all square roots to 150