Question

The area of a square is 200ft^2, find one of its sides in simplest radical form.

Answer 1

Side=
`10√(2)`

Explanation:

Let one side of square be x, so we can write the area of square formula:

`Area=x^2`

Now, we know area = 200, so we find x:

`Area = x^2\\200=x^2\\x=√(200)`

To get this answer to simplest radical form, we need to know the rule shown below:

`√(a*b) =√(a) √(b)`

Let' simplify our answer:

`x=√(200) \\x=√(25*8)\\ x=√(25)√(8) \\ x=5√(8) \\x=5√(4*2) \\x=5√(4) √(2) \\x=5*2√(2)\\ x=10√(2)`

This is the simplest form since
`√(2)` can't be broken down further.