Square Root Calculator › Square root of 42
Square Root of 42
√42 ≈ 6.480741
42 is not a perfect square, so √42 is an irrational number that is approximately 6.480741. In simplified radical form, √42 = √42.
√42 lies between √36 = 6 and √49 = 7.
| Number | 42 |
| Square root (decimal) | 6.480741 |
| Simplified radical | √42 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 42
42 = 2 × 3 × 7. This is what determines the simplified radical: for √42 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √42 is already in simplest radical form as √42.
Estimating √42 by hand
√42 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 42 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.5 |
| Step 2 | 6.480769 |
| Step 3 | 6.480741 |
After 3 steps the estimate is 6.480741, matching √42 ≈ 6.480741.
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Frequently asked questions
Is 42 a perfect square?
No, 42 is not a perfect square, so its square root is irrational and approximately 6.480741.
What is the square root of 42 in simplest radical form?
√42 = √42 in simplest radical form.