Square root of 8
√8 ≈ 2.8284. The square root of 8 is about 2.8284, which simplifies to 2√2. 8 is not a perfect square, so √8 is irrational: its decimals never end or repeat.
| Value | 2.82842712 |
|---|---|
| Rounded | 2.8 (1 dp) · 2.83 (2 dp) · 2.828 (3 dp) |
| Simplest radical form | 2√2 |
| Perfect square? | No — between 2² = 4 and 3² = 9 |
| 8 squared | 64 |
Estimating √8 in your head
Start from the nearest perfect square, 3² = 9. 8 is 1 less than that. Divide the difference by twice the root, 6, and subtract it:
√8 ≈ 3 − 1 ÷ 6 ≈ 2.833
The true value is 2.8284, so the one-step estimate is off by about 0.005. The estimate always comes out slightly high, and it is closest when 8 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √8
Find the largest perfect square that divides 8: it is 4, since 8 = 4 × 2. Take its root outside: √8 = √4 × √2 = 2√2.
Frequently asked questions
What is the square root of 8?
The square root of 8 is about 2.8284, which simplifies to 2√2. 8 is not a perfect square, so √8 is irrational: its decimals never end or repeat.
Is 8 a perfect square?
No. It lies between 2² = 4 and 3² = 9.
What is √8 in simplest radical form?
√8 = √(4 × 2) = 2√2.
Practise estimating square rootsNearby: √7 · √9 · all square roots to 150