Square root of 83
√83 ≈ 9.1104. The square root of 83 is about 9.1104. 83 is not a perfect square, so √83 is irrational: its decimals never end or repeat.
| Value | 9.11043358 |
|---|---|
| Rounded | 9.1 (1 dp) · 9.11 (2 dp) · 9.110 (3 dp) |
| Simplest radical form | √83 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 83 squared | 6,889 |
Estimating √83 in your head
Start from the nearest perfect square, 9² = 81. 83 is 2 more than that. Divide the difference by twice the root, 18, and add it:
√83 ≈ 9 + 2 ÷ 18 ≈ 9.111
The true value is 9.1104, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 83 is near a perfect square. The method is explained in estimating square roots in your head.
Can √83 be simplified?
No. 83 has no perfect-square factor besides 1, so √83 is already in simplest radical form.
Frequently asked questions
What is the square root of 83?
The square root of 83 is about 9.1104. 83 is not a perfect square, so √83 is irrational: its decimals never end or repeat.
Is 83 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √83 in simplest radical form?
√83 is already in simplest form: 83 has no square factor other than 1.
Practise estimating square rootsNearby: √82 · √84 · all square roots to 150