Square root of 82
√82 ≈ 9.0554. The square root of 82 is about 9.0554. 82 is not a perfect square, so √82 is irrational: its decimals never end or repeat.
| Value | 9.05538514 |
|---|---|
| Rounded | 9.1 (1 dp) · 9.06 (2 dp) · 9.055 (3 dp) |
| Simplest radical form | √82 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 82 squared | 6,724 |
Estimating √82 in your head
Start from the nearest perfect square, 9² = 81. 82 is 1 more than that. Divide the difference by twice the root, 18, and add it:
√82 ≈ 9 + 1 ÷ 18 ≈ 9.056
The true value is 9.0554, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 82 is near a perfect square. The method is explained in estimating square roots in your head.
Can √82 be simplified?
No. 82 has no perfect-square factor besides 1, so √82 is already in simplest radical form.
Frequently asked questions
What is the square root of 82?
The square root of 82 is about 9.0554. 82 is not a perfect square, so √82 is irrational: its decimals never end or repeat.
Is 82 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √82 in simplest radical form?
√82 is already in simplest form: 82 has no square factor other than 1.
Practise estimating square rootsNearby: √81 · √83 · all square roots to 150