Square root of 89
√89 ≈ 9.434. The square root of 89 is about 9.434. 89 is not a perfect square, so √89 is irrational: its decimals never end or repeat.
| Value | 9.43398113 |
|---|---|
| Rounded | 9.4 (1 dp) · 9.43 (2 dp) · 9.434 (3 dp) |
| Simplest radical form | √89 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 89 squared | 7,921 |
Estimating √89 in your head
Start from the nearest perfect square, 9² = 81. 89 is 8 more than that. Divide the difference by twice the root, 18, and add it:
√89 ≈ 9 + 8 ÷ 18 ≈ 9.444
The true value is 9.434, so the one-step estimate is off by about 0.01. The estimate always comes out slightly high, and it is closest when 89 is near a perfect square. The method is explained in estimating square roots in your head.
Can √89 be simplified?
No. 89 has no perfect-square factor besides 1, so √89 is already in simplest radical form.
Frequently asked questions
What is the square root of 89?
The square root of 89 is about 9.434. 89 is not a perfect square, so √89 is irrational: its decimals never end or repeat.
Is 89 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √89 in simplest radical form?
√89 is already in simplest form: 89 has no square factor other than 1.
Practise estimating square rootsNearby: √88 · √90 · all square roots to 150