Square Root Calculator › Square root of 5
Square Root of 5
√5 ≈ 2.236068
5 is not a perfect square, so √5 is an irrational number that is approximately 2.236068. In simplified radical form, √5 = √5.
√5 lies between √4 = 2 and √9 = 3.
| Number | 5 |
| Square root (decimal) | 2.236068 |
| Simplified radical | √5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 5
5 = 5. This is what determines the simplified radical: for √5 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √5 is already in simplest radical form as √5.
Estimating √5 by hand
√5 falls between √4 = 2 and √9 = 3, so it starts at 2.something. The Babylonian method refines that guess by averaging it with 5 ÷ the guess:
| Step | Estimate |
| Start | 2 |
| Step 1 | 2.25 |
| Step 2 | 2.236111 |
| Step 3 | 2.236068 |
After 3 steps the estimate is 2.236068, matching √5 ≈ 2.236068.
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Frequently asked questions
Is 5 a perfect square?
No, 5 is not a perfect square, so its square root is irrational and approximately 2.236068.
What is the square root of 5 in simplest radical form?
√5 = √5 in simplest radical form.