Square root of 10
√10 ≈ 3.1623. The square root of 10 is about 3.1623. 10 is not a perfect square, so √10 is irrational: its decimals never end or repeat.
| Value | 3.16227766 |
|---|---|
| Rounded | 3.2 (1 dp) · 3.16 (2 dp) · 3.162 (3 dp) |
| Simplest radical form | √10 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 10 squared | 100 |
Estimating √10 in your head
Start from the nearest perfect square, 3² = 9. 10 is 1 more than that. Divide the difference by twice the root, 6, and add it:
√10 ≈ 3 + 1 ÷ 6 ≈ 3.167
The true value is 3.1623, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 10 is near a perfect square. The method is explained in estimating square roots in your head.
Can √10 be simplified?
No. 10 has no perfect-square factor besides 1, so √10 is already in simplest radical form.
Frequently asked questions
What is the square root of 10?
The square root of 10 is about 3.1623. 10 is not a perfect square, so √10 is irrational: its decimals never end or repeat.
Is 10 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √10 in simplest radical form?
√10 is already in simplest form: 10 has no square factor other than 1.
Practise estimating square rootsNearby: √9 · √11 · all square roots to 150