Simplify the following expressions.
i. 
ii. 
iii. 
iv. 
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
Couldn't generate an explanation.
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on the number line, upto 3 decimal places.
