(2)/(2+√(7) )

Question

`(2)/(2+√(7) )`

Answer 1

`\huge\boxed{\sf (2√(7)-4 )/(3)}`

Explanation:

This is a rationalizing denominator question.

Given expression:

`= \displaystyle (2)/(2+√(7) ) \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - √(7) \\\\= (2)/(2+√(7) ) * (2-√(7) )/(2-√(7) ) \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= (2(2-√(7)) )/((2)^2-(√(7))^2 ) \\\\= (4-2√(7) )/(4-7) \\\\= (4-2√(7) )/(-3) \\\\= (-(4-2√(7)) )/(3) \\\\= (2√(7)-4 )/(3) \\\\\rule[225]{225}{2}`