Question

Find the value if x and simplify completely

Answer 1

`x = 9 √(10)`

Explanation:

By Geometric mean property:

`y = √(3 * 27) \\ = √(81) \\ y = 9 \\ by \: pythagors \: theorem : \\ x = \sqrt{ {27}^(2) + {9}^(2) } \\ = \sqrt{(9 * 3)^(2) + {9}^(2) } \\ = \sqrt{ {9}^(2) * {3}^(2) + { {9}^(2) } } \\ = \sqrt{ {9}^(2) ( {3}^(2) + 1)} \\ = 9 √(9 + 1) \\ x = 9 √(10)`