Square root of 98
√98 ≈ 9.8995. The square root of 98 is about 9.8995, which simplifies to 7√2. 98 is not a perfect square, so √98 is irrational: its decimals never end or repeat.
| Value | 9.89949494 |
|---|---|
| Rounded | 9.9 (1 dp) · 9.90 (2 dp) · 9.899 (3 dp) |
| Simplest radical form | 7√2 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 98 squared | 9,604 |
Estimating √98 in your head
Start from the nearest perfect square, 10² = 100. 98 is 2 less than that. Divide the difference by twice the root, 20, and subtract it:
√98 ≈ 10 − 2 ÷ 20 ≈ 9.9
The true value is 9.8995, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 98 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √98
Find the largest perfect square that divides 98: it is 49, since 98 = 49 × 2. Take its root outside: √98 = √49 × √2 = 7√2.
Frequently asked questions
What is the square root of 98?
The square root of 98 is about 9.8995, which simplifies to 7√2. 98 is not a perfect square, so √98 is irrational: its decimals never end or repeat.
Is 98 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √98 in simplest radical form?
√98 = √(49 × 2) = 7√2.
Practise estimating square rootsNearby: √97 · √99 · all square roots to 150