Square root of 108
√108 ≈ 10.3923. The square root of 108 is about 10.3923, which simplifies to 6√3. 108 is not a perfect square, so √108 is irrational: its decimals never end or repeat.
| Value | 10.39230485 |
|---|---|
| Rounded | 10.4 (1 dp) · 10.39 (2 dp) · 10.392 (3 dp) |
| Simplest radical form | 6√3 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 108 squared | 11,664 |
Estimating √108 in your head
Start from the nearest perfect square, 10² = 100. 108 is 8 more than that. Divide the difference by twice the root, 20, and add it:
√108 ≈ 10 + 8 ÷ 20 ≈ 10.4
The true value is 10.3923, so the one-step estimate is off by about 0.008. The estimate always comes out slightly high, and it is closest when 108 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √108
Find the largest perfect square that divides 108: it is 36, since 108 = 36 × 3. Take its root outside: √108 = √36 × √3 = 6√3.
Frequently asked questions
What is the square root of 108?
The square root of 108 is about 10.3923, which simplifies to 6√3. 108 is not a perfect square, so √108 is irrational: its decimals never end or repeat.
Is 108 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √108 in simplest radical form?
√108 = √(36 × 3) = 6√3.
Practise estimating square rootsNearby: √107 · √109 · all square roots to 150