Multiply

i. √3(√7 – √3)

ii. (√5 – √7)√2

iii. (3√2 – √3)(4√3 – √2)

i. √3(√7 – √3)

=√3 × √7 – √3 × √3

[∵√a(√b–√c)=√a×√b–√a×√c]

=√21 – 3 [∵√a×√b=√ab and √a×√a=a]

⇒ √3(√7 – √3) = –3 + √21

ii. (√5 – √7)√2

=√5 × √2 – √7 × √2

[∵√a(√b–√c)=√a×√b–√a×√c]

=√10 – √14 [∵√a×√b=√ab]

⇒ (√5 – √7)√2 =√10 – √14

iii. (3√2 – √3)(4√3 – √2)

=3√2(4√3 – √2) – √3(4√3 – √2)

=3√2×4√3 – 3√2×√2 – √3×4√3 + √3×√2

[∵√a(√b–√c)=√a×√b–√a×√c]

=12√6 – 3×2 – 4×3 + √6 [∵√a×√b=√ab]

=12√6 – 6 – 12 + √6

=13√6 – 18

⇒ (3√2 – √3)(4√3 – √2) = 13√6 – 18