निम्नलिखित व्यंजकों में से प्रत्येक व्यंजक को सरल कीजिए :
(i) `(3+sqrt(3)) (2+sqrt(2)` , (ii) `(3+sqrt(3)) (3-sqrt(3))`
(iii) `(sqrt(5) + sqrt(2))^(2)`
(iv) `(sqrt(5) - sqrt(2)) (sqrt(5) + sqrt(2))`

Explanation

(i) `(3+sqrt(3)) (2+sqrt(2))`
`= 3(2+sqrt(2)) + sqrt(3)(2+sqrt(2))`
`= 6+3sqrt(2) + 2sqrt(3) + sqrt(6)`
(ii) `(3+sqrt(3))(3-sqrt(3)) = (3)^(2) - (sqrt(3))^(2)`
`= 9- 3 = 6`
(iii) `(sqrt(5) + sqrt(2))^(2) = (sqrt(5))^(2) + (sqrt(2))^(2)+ 2(sqrt(5)) (sqrt(2))`
`= 5 + 2 + 2sqrt(10) = 7 + 2sqrt(10)`
(iv) `(sqrt(5) - sqrt(2)) (sqrt(5) + sqrt(2)) = (sqrt(5))^(2) - (sqrt(2))^(2)`
`= 5 - 2 = 3`