Define a surd and find the length of one side of a 50cm^2 square shape in surd form

i. A surd is an irrational number i.e. a non-whole number that can be represented as a square root, cube root etc.

ii. If the area of the square shape is 50cm^2, then we know that the length multiplied by the width will give us the area. As the shape is a square, the length and width are the same value. Therefore, xx = area; x^2 = 50, x = sqrt(50), x = sqrt(252) note: we are looking for two factors of 50 where one factor that can be square rooted is rational and the the other factor is the lowest irrational number. Therefore x = sqrt(25)sqrt(2), x = 5sqrt(2)