Square root of 85
√85 ≈ 9.2195. The square root of 85 is about 9.2195. 85 is not a perfect square, so √85 is irrational: its decimals never end or repeat.
| Value | 9.21954446 |
|---|---|
| Rounded | 9.2 (1 dp) · 9.22 (2 dp) · 9.220 (3 dp) |
| Simplest radical form | √85 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 85 squared | 7,225 |
Estimating √85 in your head
Start from the nearest perfect square, 9² = 81. 85 is 4 more than that. Divide the difference by twice the root, 18, and add it:
√85 ≈ 9 + 4 ÷ 18 ≈ 9.222
The true value is 9.2195, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 85 is near a perfect square. The method is explained in estimating square roots in your head.
Can √85 be simplified?
No. 85 has no perfect-square factor besides 1, so √85 is already in simplest radical form.
Frequently asked questions
What is the square root of 85?
The square root of 85 is about 9.2195. 85 is not a perfect square, so √85 is irrational: its decimals never end or repeat.
Is 85 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √85 in simplest radical form?
√85 is already in simplest form: 85 has no square factor other than 1.
Practise estimating square rootsNearby: √84 · √86 · all square roots to 150