Question

Solve for x, y, and z. Enter the integer that is under each radical.

Answer 1

`x=√(10)`

`y = \sqrt {14}`

`z = \sqrt {35}`

Explanation:

By geometric mean theorem:

`x=√(2* 5)`

`x=√(10)`

By Pythagoras Theorem:

`y^2 = x^2 + 2^2`

`y^2 = (√(10)) ^2 + 2^2`

`y^2 = 10 + 4`

`y^2 = 14`

`y = \sqrt {14}`

Again by Pythagoras Theorem:

`z^2 = x^2 + 5^2`

`z^2 = (√(10)) ^2 + 5^2`

`z^2 = 10 + 25`

`z^2 = 35`

`z = \sqrt {35}`