Square root of 119
√119 ≈ 10.9087. The square root of 119 is about 10.9087. 119 is not a perfect square, so √119 is irrational: its decimals never end or repeat.
| Value | 10.90871211 |
|---|---|
| Rounded | 10.9 (1 dp) · 10.91 (2 dp) · 10.909 (3 dp) |
| Simplest radical form | √119 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 119 squared | 14,161 |
Estimating √119 in your head
Start from the nearest perfect square, 11² = 121. 119 is 2 less than that. Divide the difference by twice the root, 22, and subtract it:
√119 ≈ 11 − 2 ÷ 22 ≈ 10.909
The true value is 10.9087, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 119 is near a perfect square. The method is explained in estimating square roots in your head.
Can √119 be simplified?
No. 119 has no perfect-square factor besides 1, so √119 is already in simplest radical form.
Frequently asked questions
What is the square root of 119?
The square root of 119 is about 10.9087. 119 is not a perfect square, so √119 is irrational: its decimals never end or repeat.
Is 119 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √119 in simplest radical form?
√119 is already in simplest form: 119 has no square factor other than 1.
Practise estimating square rootsNearby: √118 · √120 · all square roots to 150