We know that- Hence = a 6 + 6a 5 b + 15a 4 b 2 + 20a 3 b 3 + 15a 2 b 4 + 6ab 5 + b 6 Thus, (a + b) 6 = a 6 + 6a 5 b + 15a 4 b 2 + 20a 3 b 3 + 15a 2 b 4 + 6ab 5 + b 6 Replacing b with -b (a +(-b)) 6 = a 6 + 6a 5 (-b) + 15a 4 (-b) 2 + 20a 3 (-b) 3 + 15a 2 (-b) 4 + 6a(-b) 5 + (-b) 6 (a - b) 6 = a 6 - 6a 5 b + 15a 4 b 2 - 20a 3 b 3 + 15a 2 b 4 - 6ab 5 + b 6 Now, (a + b) 6 - (a - b) 6 = (a 6 + 6a 5 b + 15a 4 b 2 + 20a 3 b 3 + 15a 2 b 4 + 6ab 5 + b 6 ) - (a 6 - 6a 5 b + 15a 4 b 2 - 20a 3 b 3 + 15a 2 b 4 - 6ab 5 + b 6 ) = 2(6a 5 b + 20a 3 b 3 + 6ab 5 ) Putting a = √3 & b = √2, we get- ( √3 + √2 ) 6 - ( √3 - √2 ) 6 = 2[6(√3) 5 ( √2 ) + 20(√3) 3 ( √2 ) 3 + 6(√3)( √2 ) 5 ] = 2[6(9√3)(√2) + 20(3√3)(2√2) + 6(√3)(4√2)] = 2[54√6 + 120√6 + 24√6] = 2[198√6] = 396√6