Square root of 92
√92 ≈ 9.5917. The square root of 92 is about 9.5917, which simplifies to 2√23. 92 is not a perfect square, so √92 is irrational: its decimals never end or repeat.
| Value | 9.59166305 |
|---|---|
| Rounded | 9.6 (1 dp) · 9.59 (2 dp) · 9.592 (3 dp) |
| Simplest radical form | 2√23 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 92 squared | 8,464 |
Estimating √92 in your head
Start from the nearest perfect square, 10² = 100. 92 is 8 less than that. Divide the difference by twice the root, 20, and subtract it:
√92 ≈ 10 − 8 ÷ 20 ≈ 9.6
The true value is 9.5917, so the one-step estimate is off by about 0.008. The estimate always comes out slightly high, and it is closest when 92 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √92
Find the largest perfect square that divides 92: it is 4, since 92 = 4 × 23. Take its root outside: √92 = √4 × √23 = 2√23.
Frequently asked questions
What is the square root of 92?
The square root of 92 is about 9.5917, which simplifies to 2√23. 92 is not a perfect square, so √92 is irrational: its decimals never end or repeat.
Is 92 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √92 in simplest radical form?
√92 = √(4 × 23) = 2√23.
Practise estimating square rootsNearby: √91 · √93 · all square roots to 150