Square root of 117
√117 ≈ 10.8167. The square root of 117 is about 10.8167, which simplifies to 3√13. 117 is not a perfect square, so √117 is irrational: its decimals never end or repeat.
| Value | 10.81665383 |
|---|---|
| Rounded | 10.8 (1 dp) · 10.82 (2 dp) · 10.817 (3 dp) |
| Simplest radical form | 3√13 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 117 squared | 13,689 |
Estimating √117 in your head
Start from the nearest perfect square, 11² = 121. 117 is 4 less than that. Divide the difference by twice the root, 22, and subtract it:
√117 ≈ 11 − 4 ÷ 22 ≈ 10.818
The true value is 10.8167, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 117 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √117
Find the largest perfect square that divides 117: it is 9, since 117 = 9 × 13. Take its root outside: √117 = √9 × √13 = 3√13.
Frequently asked questions
What is the square root of 117?
The square root of 117 is about 10.8167, which simplifies to 3√13. 117 is not a perfect square, so √117 is irrational: its decimals never end or repeat.
Is 117 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √117 in simplest radical form?
√117 = √(9 × 13) = 3√13.
Practise estimating square rootsNearby: √116 · √118 · all square roots to 150