Rationalise the denominator 1÷(7+5√2).

 Given that 1÷7+5√2

= 1/(7+5√2)

Multiplying numerator and denominator by

7-5√2 , we get,

{1×(7-5√2)}/{(7+5√2)(7-5√2)}

=(7-5√2)/{7²-(5√2)²}.  

[By using (a+b)(a-b)=a²-b²]

=(7-5√2)/(49-50)

=(7-5√2)/(-1) = -(7-5√2) =-7+5√2.  Ans.