Exact
16
Square Root of 256
Answer
The square root of 256 is 16. This is a perfect square, so the root is an integer.
Decimal
16
Formula
√256 = 16
Worked steps
1
Definition
The square root of 256 is the non-negative number that, when multiplied by itself, gives 256. Check: 16 × 16 = 256.
2
Calculator method
Press the √ button, type 256, press =. Result: 16.
3
Why it is a perfect square
256 sits between 256 and 289, so √256 is between 16 and 17. In fact 16² = 256 exactly.
About this value
The square root of 256 is the integer 16. Perfect squares like 144, 169, and 256 produce clean integer roots. 256 = 16² = 2⁸. Common in computer science as the number of values in a byte.
Frequently asked questions
What is square root of 256?
Square Root of 256 equals 16 as an exact value, or 16 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
How do I compute it without a calculator?
Use the estimate-and-refine method. For 256, find two perfect squares it sits between, then narrow down. Or use the long-division algorithm taught in school for square roots.
Is the square root rational or irrational?
Rational — it is a whole number because the input is a perfect square. Examples of other perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100.
How do I simplify a square root?
Find the largest perfect-square factor of the number, take its root out, leave the rest under the radical. Example: √72 = √(36 × 2) = 6√2. If the input is already a perfect square, the root is a clean integer.