Square Root Calculator › Square root of 98
Square Root of 98
√98 ≈ 9.899495
98 is not a perfect square, so √98 is an irrational number that is approximately 9.899495. In simplified radical form, √98 = 7√2.
√98 lies between √81 = 9 and √100 = 10.
| Number | 98 |
| Square root (decimal) | 9.899495 |
| Simplified radical | 7√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 98
98 = 2 × 7^2. This is what determines the simplified radical: for √98 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √98 = 7√2.
Estimating √98 by hand
√98 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 98 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.944444 |
| Step 2 | 9.899597 |
| Step 3 | 9.899495 |
After 3 steps the estimate is 9.899495, matching √98 ≈ 9.899495.
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Frequently asked questions
Is 98 a perfect square?
No, 98 is not a perfect square, so its square root is irrational and approximately 9.899495.
What is the square root of 98 in simplest radical form?
√98 = 7√2 in simplest radical form.