When the square root of a number is a whole number, this number is called a perfect square. ... Not all square roots are whole numbers. Many square roots are irrational numbers, meaning there is no rational number equivalent
Very good question, i’ll try to answer this as best as I can so here we go hope you enjoy
All rational numbers have the fraction form , a b , where a and b are integers(≠0 b ≠ 0 ).
My question is: for what a and b does the fraction have rational square root? The simple answer would be when both are perfect squares, but if two perfect squares are multiplied by a common integer n , the result may not be two perfect squares. Like: 49→818 4 9 → 8 18
And intuitively, without factoring, =8 a = 8 and =18 b = 18 must qualify by some standard to have a rational square root.
Once this is solved, can this be extended to any degree of roots? Like for what a and b does the fraction have rational n th root?
