Question

can anyone help, thanks

Answer 1

Answer:

14) (√5 - √3)/√80 + √48 - √27 - √45

=> (√5-√3)/(√16×5) +√16×3 -√9×3 -√9×5)

=> √5 - √3 / (4√5 + 4√3 - 3√3 - 3√5)

=> √5 - √3 /√5 + √3

=> (√5-√3)²/(√5+√3)(√5-√3) [ multiply both numerator and denominator by the conjugate of the denominator ie √5-√3 ]

=> (5 + 3 - 2√15)/(√5)²-(√3)²

=> (8 - 2√15)/(5 - 3)

=> 2(4-√15)/2

=> 4 - √15

now on comparing 4 - √15 with

p + q√15 as below,

4 + (-1)√15

p + q√15

p= 4 and q = -1