Question

Find the value of z and
simplify completely.
4
16
х
Z=
= [? ]V[]

Answer 1

`4 √(5)`

Explanation:

By geometric mean property:

`y = √(16 * 4) \\ \\ y = √(64) \\ \\ y = 8 \\ \\ by \: pythagoras \: theorem: \\ \\ {z}^(2) = {y}^(2) + {4}^(2) \\ \\ {z}^(2) = {8}^(2) + {4}^(2) \\ \\ {z}^(2) = 64 + 16 \\ \\ {z}^(2) = 80 \\ \\ z = √(80) \\ \\ z = √(16 * 5) \\ \\ z = 4 √(5)`