What is the length of the missing side of the triangle in simplest radical form? One side is 10cm and one side is 6cm. I know that the answer is 2 square root of 34 cm but I would really like to learn how to work through the problem using the Pythagorean Theorem please.

Answer 1

I assume you meant to say that the triangle is also right-angled, and that the missing side is the hypotenuse.

h^2 = 10^2 + 6^2
= 100 + 3 = 136
h = √136

they expect you to reduce √136 to a radical expression in lowest terms
√136 = √4 * √34
= 2√34

√k can only be reduced if k contains one or more factors which are perfect squares, e.g
√125 = √25 * √5 = 5√5
√588 = √4 * √147
= √4 * √49 * √3 = 2*7√3 = 14√3
I could have recognized also that √588 = √196*√3 = 14√3

but √15 = √3 * √5 is of no use, since neither 3 or 5 are perfect squares.