Why cant you assume that a number is irrational because it is expressed using the square root symbol?

Answer 1

Well, for example, the square root of 4 is 2, which is a rational number. As long as the number which is being square rooted is not a square number itself (i.e. 1, 4, 9, 16 etc.), then it will be irrational.

So.....

the square roots of 49, 100, 196, for example, are all rational numbers (7, 10 and 14 respectively.)

They do not have to be integers. The square of of any rational number automatically has a rational square root eg the square root of 77.41792 is 77.4179 . Rational means expressable as a ratio of integers: 77.4179 is 774179/10000 .