Square root of 118
√118 ≈ 10.8628. The square root of 118 is about 10.8628. 118 is not a perfect square, so √118 is irrational: its decimals never end or repeat.
| Value | 10.86278049 |
|---|---|
| Rounded | 10.9 (1 dp) · 10.86 (2 dp) · 10.863 (3 dp) |
| Simplest radical form | √118 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 118 squared | 13,924 |
Estimating √118 in your head
Start from the nearest perfect square, 11² = 121. 118 is 3 less than that. Divide the difference by twice the root, 22, and subtract it:
√118 ≈ 11 − 3 ÷ 22 ≈ 10.864
The true value is 10.8628, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 118 is near a perfect square. The method is explained in estimating square roots in your head.
Can √118 be simplified?
No. 118 has no perfect-square factor besides 1, so √118 is already in simplest radical form.
Frequently asked questions
What is the square root of 118?
The square root of 118 is about 10.8628. 118 is not a perfect square, so √118 is irrational: its decimals never end or repeat.
Is 118 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √118 in simplest radical form?
√118 is already in simplest form: 118 has no square factor other than 1.
Practise estimating square rootsNearby: √117 · √119 · all square roots to 150