Solution
The side of a square is 'a' cm.
$$\left(Diagonal\right)^2\ =\ a^2\ +\ a^2$$ [According to the pythagoras theorem.]
$$\left(Diagonal\right)^2\ =\ 2a^2$$
$$Diagonal=\sqrt{\ 2}a$$
Ratio of its diagonal to its side = $$\sqrt{\ 2}a : a$$
= $$\sqrt{\ 2} : 1$$
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