The square root of 61 is not a rational number. To understand why, we need to look at the definition of rational numbers. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero.
The square root of 61, written as √61, is an irrational number because it cannot be simplified into a fraction of two integers. In fact, when calculated, √61 is approximately 7.81, which cannot be accurately represented as a simple fraction. Since it has a non-repeating, non-terminating decimal representation, it confirms its status as an irrational number.
Moreover, 61 is not a perfect square; the square roots of perfect squares like 1, 4, 9, 16, 25, 36, 49, and 64 are whole numbers. Since 61 falls between two perfect squares (49 and 64), its square root does not yield a whole number, hence reinforcing that √61 is not rational.