Square root of 96
√96 ≈ 9.798. The square root of 96 is about 9.798, which simplifies to 4√6. 96 is not a perfect square, so √96 is irrational: its decimals never end or repeat.
| Value | 9.79795897 |
|---|---|
| Rounded | 9.8 (1 dp) · 9.80 (2 dp) · 9.798 (3 dp) |
| Simplest radical form | 4√6 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 96 squared | 9,216 |
Estimating √96 in your head
Start from the nearest perfect square, 10² = 100. 96 is 4 less than that. Divide the difference by twice the root, 20, and subtract it:
√96 ≈ 10 − 4 ÷ 20 ≈ 9.8
The true value is 9.798, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 96 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √96
Find the largest perfect square that divides 96: it is 16, since 96 = 16 × 6. Take its root outside: √96 = √16 × √6 = 4√6.
Frequently asked questions
What is the square root of 96?
The square root of 96 is about 9.798, which simplifies to 4√6. 96 is not a perfect square, so √96 is irrational: its decimals never end or repeat.
Is 96 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √96 in simplest radical form?
√96 = √(16 × 6) = 4√6.
Practise estimating square rootsNearby: √95 · √97 · all square roots to 150