Question

Rationalise the denominator and simplify

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Answer 1

We need to rationalize the denominator of the following expressions and simplify them.

(1)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(2)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(3)

Here,

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(4)

Here,

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(5)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(6)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(7)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(8)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(9)

Multiplying both numerator and denominator by the rationalizing factorof the denominator, we get:

Hence,

(10)

Taking L.C.M., we get:

Hence,

(11)

Multiplying both numerator and denominator of each term by the rationalizing factor of its denominator, we get:

Hence,

(12)

Multiplying both numerator and denominator of each term by the rationalizing factor of its denominator, we get:

Hence,

(13)

Multiplying both numerator and denominator of each term by the rationalizing factor of its denominator, we get:

Hence,