We have three pythagoras:
4² + y² = z²
16² + y² = x²
x² + z² = 20²
Now let's think:
4² + y² = z²
y² = z² - 4²
16² + y² = x²
16² + z² - 4² = x²
x² + z² = 20²
16² + z²- 4² + z² = 20²
2z² = 20² - 16² + 4²
2z² = (2.10)² - (2^4)² + (2²)²
2z² = 2².10² - 2^8 + 2^4
z² = 2.10² - 2^7 + 2^3
z² = 200 - 128 + 8
z² = 208 - 128
z² = 80
z = √80
80 | 2
40 | 2
20 | 2
10 | 2
5 | 5
1
80 = 5.2^4
So
√80 = 4√5
z = 4√5
