Square root of 120
√120 ≈ 10.9545. The square root of 120 is about 10.9545, which simplifies to 2√30. 120 is not a perfect square, so √120 is irrational: its decimals never end or repeat.
| Value | 10.95445115 |
|---|---|
| Rounded | 11.0 (1 dp) · 10.95 (2 dp) · 10.954 (3 dp) |
| Simplest radical form | 2√30 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 120 squared | 14,400 |
Estimating √120 in your head
Start from the nearest perfect square, 11² = 121. 120 is 1 less than that. Divide the difference by twice the root, 22, and subtract it:
√120 ≈ 11 − 1 ÷ 22 ≈ 10.955
The true value is 10.9545, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 120 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √120
Find the largest perfect square that divides 120: it is 4, since 120 = 4 × 30. Take its root outside: √120 = √4 × √30 = 2√30.
Frequently asked questions
What is the square root of 120?
The square root of 120 is about 10.9545, which simplifies to 2√30. 120 is not a perfect square, so √120 is irrational: its decimals never end or repeat.
Is 120 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √120 in simplest radical form?
√120 = √(4 × 30) = 2√30.
Practise estimating square rootsNearby: √119 · √121 · all square roots to 150