Square root of 91
√91 ≈ 9.5394. The square root of 91 is about 9.5394. 91 is not a perfect square, so √91 is irrational: its decimals never end or repeat.
| Value | 9.53939201 |
|---|---|
| Rounded | 9.5 (1 dp) · 9.54 (2 dp) · 9.539 (3 dp) |
| Simplest radical form | √91 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 91 squared | 8,281 |
Estimating √91 in your head
Start from the nearest perfect square, 10² = 100. 91 is 9 less than that. Divide the difference by twice the root, 20, and subtract it:
√91 ≈ 10 − 9 ÷ 20 ≈ 9.55
The true value is 9.5394, so the one-step estimate is off by about 0.011. The estimate always comes out slightly high, and it is closest when 91 is near a perfect square. The method is explained in estimating square roots in your head.
Can √91 be simplified?
No. 91 has no perfect-square factor besides 1, so √91 is already in simplest radical form.
Frequently asked questions
What is the square root of 91?
The square root of 91 is about 9.5394. 91 is not a perfect square, so √91 is irrational: its decimals never end or repeat.
Is 91 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √91 in simplest radical form?
√91 is already in simplest form: 91 has no square factor other than 1.
Practise estimating square rootsNearby: √90 · √92 · all square roots to 150