Question

Canh square roots be rational numbers ?

Answer 1

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

Answer 2

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?

Have a blessed day God bless.