What is the approximate diagonal distance from one corner of a 3 inch by 5 inch index card to the opposite corner

5.83 inches

Step-by-step explanation:

The card is a rectangular shaped object, drawing a diagonal from one corner to the other, divides the rectangle into two right angled triangles with the diagonals as the hypothenuse.

Using Pythagoras theorem.

c^2 = a^2 + b^2

Given;

Side a = 3

Side b = 5

Substituting the given values;

c^2 = 3^2 + 5^2

c = √ (9+25)

c = √34

c = 5.83 inches