If ‘a’ and ‘b’ are rational numbers, find the value of a and b in each of the following equations.

i.

ii.

i. Given a + b√6 =

Rationalizing the denominator,

⇒ a + b√6 =

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

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

⇒ a + b√6 =

=

= 5 + 2√6

Comparing it with a + b√6, we get

⇒ a = 5 and b = 2

ii. Given a – b√15 =

Rationalizing the denominator,

⇒ a – b√15 =

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

⇒ a – b√15 =

=

=

=

Comparing with a – b√15, we get

⇒ a = and b =