Exact
13
Square Root of 169
Answer
The square root of 169 is 13. This is a perfect square, so the root is an integer.
Decimal
13
Formula
√169 = 13
Worked steps
1
Definition
The square root of 169 is the non-negative number that, when multiplied by itself, gives 169. Check: 13 × 13 = 169.
2
Calculator method
Press the √ button, type 169, press =. Result: 13.
3
Why it is a perfect square
169 sits between 169 and 196, so √169 is between 13 and 14. In fact 13² = 169 exactly.
About this value
The square root of 169 is the integer 13. Perfect squares like 144, 169, and 256 produce clean integer roots. 169 = 13², from the Pythagorean-triple family (5, 12, 13).
Frequently asked questions
What is square root of 169?
Square Root of 169 equals 13 as an exact value, or 13 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 169, 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.