Square Root Calculator › Square root of 46
Square Root of 46
√46 ≈ 6.78233
46 is not a perfect square, so √46 is an irrational number that is approximately 6.78233. In simplified radical form, √46 = √46.
√46 lies between √36 = 6 and √49 = 7.
| Number | 46 |
| Square root (decimal) | 6.78233 |
| Simplified radical | √46 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 46
46 = 2 × 23. This is what determines the simplified radical: for √46 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √46 is already in simplest radical form as √46.
Estimating √46 by hand
√46 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 46 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.833333 |
| Step 2 | 6.78252 |
| Step 3 | 6.78233 |
After 3 steps the estimate is 6.78233, matching √46 ≈ 6.78233.
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Frequently asked questions
Is 46 a perfect square?
No, 46 is not a perfect square, so its square root is irrational and approximately 6.78233.
What is the square root of 46 in simplest radical form?
√46 = √46 in simplest radical form.