Square root of 115
√115 ≈ 10.7238. The square root of 115 is about 10.7238. 115 is not a perfect square, so √115 is irrational: its decimals never end or repeat.
| Value | 10.72380529 |
|---|---|
| Rounded | 10.7 (1 dp) · 10.72 (2 dp) · 10.724 (3 dp) |
| Simplest radical form | √115 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 115 squared | 13,225 |
Estimating √115 in your head
Start from the nearest perfect square, 11² = 121. 115 is 6 less than that. Divide the difference by twice the root, 22, and subtract it:
√115 ≈ 11 − 6 ÷ 22 ≈ 10.727
The true value is 10.7238, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 115 is near a perfect square. The method is explained in estimating square roots in your head.
Can √115 be simplified?
No. 115 has no perfect-square factor besides 1, so √115 is already in simplest radical form.
Frequently asked questions
What is the square root of 115?
The square root of 115 is about 10.7238. 115 is not a perfect square, so √115 is irrational: its decimals never end or repeat.
Is 115 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √115 in simplest radical form?
√115 is already in simplest form: 115 has no square factor other than 1.
Practise estimating square rootsNearby: √114 · √116 · all square roots to 150