There are infinitely many Irrational Numbers between 4 and 6, so the article "the" is used incorrectly. For example, 4.75933201865... is irrational, so is pi + 1 or e + 3.
There are infinite irrational numbers between 1 and 6.
There are an infinite number of irrational numbers between 2 and 4. See the link below for the definition of irrational numbers. The two most popular irrational numbers between 2 and 4 are pi (3.14159...) and e (2.71828...).
4*sqrt(2) Rational multiples of irrational numbers are irrational. sqrt(2) is about 1.414, and 5/4 = 1.25 < 1.414... < 1.75 = 7/4 so 4*sqrt(2) is between 5 and 7, and is irrational.
The square root of 3 is an irrational number
The square root of 3 is an irrational number
Irrational numbers are infinitely dense. Between any two numbers, there are infinitely many irrational numbers. So if it was claimed that some irrational, x, was the closest irrational to 6, it is possible to find an infinite number of irrationals between 6 and x. Each one of these infinite number of irrationals would be closer to 6 than x. So the search for the nearest irrational must fail.
3.1459...
sqrt(27)
Not necessarily. The cube roots of 4, 6 and 9 are all irrational (and different). But their product is 6, not just rational, but an integer.
4.6 is rational.
yes there is, it's between every number
3 squared is 9 and 4 squared is 16, so the square root of any whole number between 9 and 16 will be irrational.