# Rationalisation......sounds easy

**Number Theory**Level 5

\[ \large \frac{1}{ \sqrt[7]{531441} + \sqrt[7]{472392} + \sqrt[7]{419904} + \sqrt[7]{373248} + \sqrt[7]{331776} + \sqrt[7]{294912} + \sqrt[7]{262144} } \]

After rationalizing the denominator of the above number. It appears in the form \( \large \frac{ \sqrt[7]{a} - \sqrt[7]{b} + \sqrt[7]{c} }{d} \)

Find \( a - b + c + d \) .

Note - \( a > b \) , gcd(a,b,c,d) = 1 .

This problem is a part of the sets - 3's & 4's & " N " for number theory

Follw me for more questions in the future.