Square Root Calculator › Square root of 70
Square Root of 70
√70 ≈ 8.3666
70 is not a perfect square, so √70 is an irrational number that is approximately 8.3666. In simplified radical form, √70 = √70.
√70 lies between √64 = 8 and √81 = 9.
| Number | 70 |
| Square root (decimal) | 8.3666 |
| Simplified radical | √70 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 70
70 = 2 × 5 × 7. This is what determines the simplified radical: for √70 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √70 is already in simplest radical form as √70.
Estimating √70 by hand
√70 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 70 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.375 |
| Step 2 | 8.366604 |
| Step 3 | 8.3666 |
After 3 steps the estimate is 8.3666, matching √70 ≈ 8.3666.
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Frequently asked questions
Is 70 a perfect square?
No, 70 is not a perfect square, so its square root is irrational and approximately 8.3666.
What is the square root of 70 in simplest radical form?
√70 = √70 in simplest radical form.