Question

A square has side length 10yd.What is the length of a diagonal of the square?Express in simplest radical form

Answer 1

`10√(2)`

Explanation:

The diagonal of a square with side s is given by the formula

`s√(2)`

So in this case the simplest radical form is

`10√(2)`

For the long story.

if d= diagonal of the square and s each of its sides

`d^2 = s^2 + s^2\\\d= √(s^2 + s^2) =√(2s^2) = √(2) √(s^2)`

But
`√(s^2)` is just
`s`

So d =
`√(2) s`