Simplify each of the following by rationalising the denominator:
i. 
ii. 
iii. 
iv. 
i.
Rationalizing the denominator by its conjugate,
⇒ 
We know that (a - √b) (a + √b) = a2 – b.
We know that (a - √b)2 = a2 – 2a√b + b.
⇒ 
⇒ 
⇒ 
⇒ 17 – 12√2
ii.
Rationalizing the denominator, we get
⇒ 
We know that (√a - √b) (√a + √b) = a – b.
We know that (√a - √b)2 = a - 2√(ab) + b.
⇒ 
⇒ 
⇒ 
⇒ 6 - √35
iii. 
Rationalizing the denominator,
⇒ 
We know that (√a - √b) (√a + √b) = a – b.
⇒ 
⇒ 
iv.
Rationalizing the denominator,
⇒ 
We know that (√a - √b) (√a + √b) = a – b.
⇒ 
= 
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is represented by p. But we say that π is an irrational number. Why?
ii. 
iv. 
vi. 