Square root of 116
√116 ≈ 10.7703. The square root of 116 is about 10.7703, which simplifies to 2√29. 116 is not a perfect square, so √116 is irrational: its decimals never end or repeat.
| Value | 10.77032961 |
|---|---|
| Rounded | 10.8 (1 dp) · 10.77 (2 dp) · 10.770 (3 dp) |
| Simplest radical form | 2√29 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 116 squared | 13,456 |
Estimating √116 in your head
Start from the nearest perfect square, 11² = 121. 116 is 5 less than that. Divide the difference by twice the root, 22, and subtract it:
√116 ≈ 11 − 5 ÷ 22 ≈ 10.773
The true value is 10.7703, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 116 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √116
Find the largest perfect square that divides 116: it is 4, since 116 = 4 × 29. Take its root outside: √116 = √4 × √29 = 2√29.
Frequently asked questions
What is the square root of 116?
The square root of 116 is about 10.7703, which simplifies to 2√29. 116 is not a perfect square, so √116 is irrational: its decimals never end or repeat.
Is 116 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √116 in simplest radical form?
√116 = √(4 × 29) = 2√29.
Practise estimating square rootsNearby: √115 · √117 · all square roots to 150