Question

Combine, and simplify the following radical expressions:

√7-5/√7+√8

Answer 1

`(√(7)-5)/(√(7)+√(8))`

Rationalize.

`-7+2√(14)+5√(7)-10√(2)`

This can be further simplified to the decimal:

-0.43006...

I hope this helps :)

Answer 2

`(√(7) - 5)/(√(7)+ √(7) )`

Rationalise the denominator:

`((√(7) - 5)(√(7) - √(8)) )/((√(7)+ √(8)) (√(7) - √(8)) )`

`= ((√(7))^2 - 5√(7) + 5√(8)- √(7)√(8) )/(7 - 8 )`

`= ((7 - 5√(7) + 10√(2)- 2√(14))/(-1 )`

`= -7 + 5√(7) - 10√(2) + 2√(14)`