Q. 64.5( 34 Votes )

# Simplify each of the following by rationalising the denominator:

i.

ii.

iii.

iv.

Answer :

i.

Rationalizing the denominator by its conjugate,

⇒

__We know that (a - √b) (a + √b) = a ^{2} – b.__

__We know that (a - √b) ^{2} = a^{2} – 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.__

⇒

=

Rate this question :

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