Simplify the foll

i. (5 + √7) (2 + √5)

We know that (a + √b) (c + √d) = ac + a√d + √b c + √b (√d).

Comparing with the given expression,

⇒ a = 5; b = 7; c = 2; d = 5

∴ (5 + √7) (2 + √5) = 5(2) + 5(√5) + √7(2) + √7(√5)

= 10 + 5√5 + 2√7 + √35

ii. (5 + √5) (5 - √5)

We know that (a + √b) (a - √b) = a² – b.

Comparing with the given expression,

⇒ a = 5; b = 5

∴ (5 + √5) (5 - √5) = 5² – (√5)²

= 25 – 5 = 20

∴ (5 + √5) (5 - √5) = 20

iii. (√3 + √7)²

We know that (√a + √b)² = a + 2√(ab) + b.

Comparing with the given expression,

⇒ a = 3; b = 7

∴ (√3 + √7)² = 3 + 2(√3) (√7) + 7

= 3 + 2(√21) + 7

= 10 + 2√21

∴ (√3 + √7)² = 10 + 2√21

iv. (√11 - √7) (√11 + √7)

We know that (√a - √b) (√a + √b) = a – b.

Comparing with the given expression,

⇒ a = 11; b = 7

∴ (√11 - √7) (√11 + √7) = 11 – 7

= 4