Let us fill up the blank:

i. a _________ number (rational/ irrational)

ii. Conjugate surd of is ________.

iii. If the product and sum of two quadratic surds is a rational number, then the surds are _________ surds.

(a) Irrational

As √11 is irrational number

Multiplying it with 5

Also get irrational number

(b) √3 + 5

Conjugate surds are surds which are having same terms but having different symbol( + to- and – to + ) in between both the terms.

(c) Conjugate Surds

While product of conjugate surds

They get square to become rational number

While sum of conjugate surds

They get cancel to become rational number