Square root of 125
√125 ≈ 11.1803. The square root of 125 is about 11.1803, which simplifies to 5√5. 125 is not a perfect square, so √125 is irrational: its decimals never end or repeat.
| Value | 11.18033989 |
|---|---|
| Rounded | 11.2 (1 dp) · 11.18 (2 dp) · 11.180 (3 dp) |
| Simplest radical form | 5√5 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 125 squared | 15,625 |
Estimating √125 in your head
Start from the nearest perfect square, 11² = 121. 125 is 4 more than that. Divide the difference by twice the root, 22, and add it:
√125 ≈ 11 + 4 ÷ 22 ≈ 11.182
The true value is 11.1803, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 125 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √125
Find the largest perfect square that divides 125: it is 25, since 125 = 25 × 5. Take its root outside: √125 = √25 × √5 = 5√5.
Frequently asked questions
What is the square root of 125?
The square root of 125 is about 11.1803, which simplifies to 5√5. 125 is not a perfect square, so √125 is irrational: its decimals never end or repeat.
Is 125 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √125 in simplest radical form?
√125 = √(25 × 5) = 5√5.
Practise estimating square rootsNearby: √124 · √126 · all square roots to 150