Square root of 97
√97 ≈ 9.8489. The square root of 97 is about 9.8489. 97 is not a perfect square, so √97 is irrational: its decimals never end or repeat.
| Value | 9.8488578 |
|---|---|
| Rounded | 9.8 (1 dp) · 9.85 (2 dp) · 9.849 (3 dp) |
| Simplest radical form | √97 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 97 squared | 9,409 |
Estimating √97 in your head
Start from the nearest perfect square, 10² = 100. 97 is 3 less than that. Divide the difference by twice the root, 20, and subtract it:
√97 ≈ 10 − 3 ÷ 20 ≈ 9.85
The true value is 9.8489, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 97 is near a perfect square. The method is explained in estimating square roots in your head.
Can √97 be simplified?
No. 97 has no perfect-square factor besides 1, so √97 is already in simplest radical form.
Frequently asked questions
What is the square root of 97?
The square root of 97 is about 9.8489. 97 is not a perfect square, so √97 is irrational: its decimals never end or repeat.
Is 97 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √97 in simplest radical form?
√97 is already in simplest form: 97 has no square factor other than 1.
Practise estimating square rootsNearby: √96 · √98 · all square roots to 150