Question

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

Answer 1

Answer:

$4 \sqrt{5}$

Step-by-step explanation:

By geometric mean property:

$y = \sqrt{16 \times 4} \\ \\ y = \sqrt{64} \\ \\ y = 8 \\ \\ by \: pythagoras \: theorem: \\ \\ {z}^{2} = {y}^{2} + {4}^{2} \\ \\ {z}^{2} = {8}^{2} + {4}^{2} \\ \\ {z}^{2} = 64 + 16 \\ \\ {z}^{2} = 80 \\ \\ z = \sqrt{80} \\ \\ z = \sqrt{16 \times 5} \\ \\ z = 4 \sqrt{5}$