Question

Under surd;
simplify the following.
1. 1 all over 2 root 3+ 5 that is 1/2√3+5.
2. 1 all over 1- root 3 all in bracket that is 1/(1-√3)^2.?

Answer 1

1 all over 2 root 3+ 5 that is 1/2√3+5 ---- strange, why not just say: 1/(2√3 + 5) ??

By "simplify" I will assume you mean "rationalize the denominator"

1/(2√3 + 5)
= 1/(2√3 + 5) * (2√3 - 5)/(2√3 - 5) <------using the conjugate
= (2√3 - 5)/(12 - 25)
= (5 - 2√3)/13

for the 2nd : 1/(1-√3)^2
first simplify (1-√3)^2
= 1 - 2√3 + 3
= 4 - 2√3

So 1/(1-√3)^2
= 1/(4 - 2√3)
proceed in the same way as I did for #1

Answer 2

1/[ 2 sqrt 3 + 5 ] * (2 sqrt 3 -5) / (2 sqrt 3 -5)

= (2 sqrt 3 - 5) / [(4*3)-25]
continue