Square root of 99
√99 ≈ 9.9499. The square root of 99 is about 9.9499, which simplifies to 3√11. 99 is not a perfect square, so √99 is irrational: its decimals never end or repeat.
| Value | 9.94987437 |
|---|---|
| Rounded | 9.9 (1 dp) · 9.95 (2 dp) · 9.950 (3 dp) |
| Simplest radical form | 3√11 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 99 squared | 9,801 |
Estimating √99 in your head
Start from the nearest perfect square, 10² = 100. 99 is 1 less than that. Divide the difference by twice the root, 20, and subtract it:
√99 ≈ 10 − 1 ÷ 20 ≈ 9.95
The true value is 9.9499, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 99 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √99
Find the largest perfect square that divides 99: it is 9, since 99 = 9 × 11. Take its root outside: √99 = √9 × √11 = 3√11.
Frequently asked questions
What is the square root of 99?
The square root of 99 is about 9.9499, which simplifies to 3√11. 99 is not a perfect square, so √99 is irrational: its decimals never end or repeat.
Is 99 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √99 in simplest radical form?
√99 = √(9 × 11) = 3√11.
Practise estimating square rootsNearby: √98 · √100 · all square roots to 150