Square Root Calculator › Square root of 400
Square Root of 400
√400 = 20
400 is a perfect square: 20 × 20 = 400. Its square root is the whole number 20.
| Number | 400 |
| Square root (decimal) | 20 |
| Simplified radical | 20 |
| Perfect square? | Yes |
| Rational? | Yes |
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Prime factorization of 400
400 = 2^4 × 5^2. This is what determines the simplified radical: for √400 you pull out one copy of any prime that appears twice.
Every prime appears an even number of times, which is exactly why 400 is a perfect square and √400 = 20 is a whole number.
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Frequently asked questions
Is 400 a perfect square?
Yes. 400 is a perfect square because 20 × 20 = 400, so √400 = 20.
What is the square root of 400 in simplest radical form?
√400 simplifies to the whole number 20.