Is a Square root a rational number? Yes or no, depends upon square root because if square root is a perfect square root means it gives Whole Number as a result which is a part of rational number, then this type of square root are called as a rational number and if square root of a number is not a perfect square means it can't give a whole number as a result, then this type of square root is called as an irrational number.Now for understanding this, we take some examples - Example 1: Is a square root of 5 is a rational number or not? Solution: square root of 5 is not a rational number because it is not a perfect square means it can't give a whole number value: √5 = 2.24 which is not a whole number and not a part of rational number .For proving this concept we initially take √5 as a rational number, now if it is a rational number, then we can define it as a a/b form - √5 = a/b Square both sides then : 5 = a/b => a2 = 5b2 Because square of a is a multiplication of 5, so, we can say that a is odd number. And when we put a = 5x in equation then it gives – (5x)2 = 5b2 = 25x2 = 5b2 => b2 = 5x2 Then we can say that b is also an odd number. And if both values are odd then number are called as a irrational number. Example 2: Is a square root of 25 is a rational number or not? Solution: We all know that 25 is a perfect square which gives whole number as a result: √25 = +5 or -5. So, we can say that square root of 25 is a rational number.