Square root of 105
√105 ≈ 10.247. The square root of 105 is about 10.247. 105 is not a perfect square, so √105 is irrational: its decimals never end or repeat.
| Value | 10.24695077 |
|---|---|
| Rounded | 10.2 (1 dp) · 10.25 (2 dp) · 10.247 (3 dp) |
| Simplest radical form | √105 |
| Perfect square? | No — between 10² = 100 and 11² = 121 |
| 105 squared | 11,025 |
Estimating √105 in your head
Start from the nearest perfect square, 10² = 100. 105 is 5 more than that. Divide the difference by twice the root, 20, and add it:
√105 ≈ 10 + 5 ÷ 20 ≈ 10.25
The true value is 10.247, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 105 is near a perfect square. The method is explained in estimating square roots in your head.
Can √105 be simplified?
No. 105 has no perfect-square factor besides 1, so √105 is already in simplest radical form.
Frequently asked questions
What is the square root of 105?
The square root of 105 is about 10.247. 105 is not a perfect square, so √105 is irrational: its decimals never end or repeat.
Is 105 a perfect square?
No. It lies between 10² = 100 and 11² = 121.
What is √105 in simplest radical form?
√105 is already in simplest form: 105 has no square factor other than 1.
Practise estimating square rootsNearby: √104 · √106 · all square roots to 150