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Does there exist an irrational number such that its square root is rational?
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
Is the square root of two fifths rational or irrational?
the square root of 2 fifths of irrational is 0.565685425
Is the product of two irrational numbers always an irrational number?
No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.
Is the square root of a decimal always an irrational number?
Not necessarily. The square root of 2.56 equals 1.6, and the square root of 0.25 equals 0.5, for two examples. If the decimal represents a rational number that is a fraction of two perfect squares, then the square root will be a rational number. The two examples I gave were 2.56 = 256/100, and 0.25 = 1/4.
The difference of two irrational numbers is an irrattinal number?
The sum, or difference, of two irrational numbers can be rational, or irrational. For example, if A = square root of 2 and B = square root of 3, both the sum and difference are irrational. If A = (1 + square root of 2), and B = square root of 2, then, while both are irrational, the difference (equal to 1) is rational.
