# 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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