Square Root Calculator › Square root of 48
Square Root of 48
√48 ≈ 6.928203
48 is not a perfect square, so √48 is an irrational number that is approximately 6.928203. In simplified radical form, √48 = 4√3.
√48 lies between √36 = 6 and √49 = 7.
| Number | 48 |
| Square root (decimal) | 6.928203 |
| Simplified radical | 4√3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 48
48 = 2^4 × 3. This is what determines the simplified radical: for √48 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √48 = 4√3.
Estimating √48 by hand
√48 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 48 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 7 |
| Step 2 | 6.928571 |
| Step 3 | 6.928203 |
After 3 steps the estimate is 6.928203, matching √48 ≈ 6.928203.
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Frequently asked questions
Is 48 a perfect square?
No, 48 is not a perfect square, so its square root is irrational and approximately 6.928203.
What is the square root of 48 in simplest radical form?
√48 = 4√3 in simplest radical form.