Question

Square root of 5 + square root of 3 the whole divided by sqaure root of 5 - square root of 3

Answer 1

The answer is 4 + √15 .

Explanation:

You have to get rid of surds in the denorminator by multiplying it with the opposite sign :

`( √(5) + √(3) )/( √(5) - √(3) )`

`= ( √(5) + √(3) )/( √(5) - √(3) ) * ( √(5) + √(3) )/( √(5) + √(3) )`

`= \frac{ {( √(5) + √(3) ) }^(2) }{( √(5) - √(3) )( √(5) + √(3)) }`

`= \frac{ {( √(5) )}^(2) + 2( √(5) )( √(3)) + {( √(3)) }^(2) }{ {( √(5)) }^(2) - { (√(3) )}^(2) }`

`= (5 + 2 √(15) + 3 )/(5 - 3)`

`= (8 + 2 √(15) )/(2)`

`= 4 + √(15)`