9514 1404 393
Answer:
√20 is not the root of a perfect square
Step-by-step explanation:
4.2^2 = 17.64
4.5^2 = 20.25
The square root of any number between these values that is not a perfect square will be irrational. This includes the roots of the integers 18, 19, or 20.
4.2 < √20 < 4.5
√20 ≈ 4.472135954999579...
_____
Of course, there are an infinite number of possibilities. It is easy enough to check to see if a rational number is a perfect square. (Its square root will have half as many decimal digits.) For example, √18.9225 is 4.35 (rational), but √18.9226 ≈ 4.350011494... is irrational.
Square roots are not the only irrational numbers. Polynomial roots, trig function values, logarithms, exponential functions are only some of the ways that irrational numbers can be specified, along with multiples or other combinations of irrational numbers such as π or <em>e</em>. These will be irrational simply because they cannot be expressed exactly as the ratio of two integers.
