Question 12: Find the rationalising factors of the following:

(i)

.

We know that the rationalizing factor of monomial is . Therefore the monomial the rationalizing factor should be

(ii)

.

We know that the rationalizing factor of monomial is . Therefore the monomial the rationalizing factor should be

(iii)

We find that

Rationalizing factor of is .

Hence is the rationalizing factor of

(iv)

We have

The conjugate of is

Therefore the rationalizing factor of is .

(v)

We know that the rationalizing factor of monomial is . Therefore the monomial the rationalizing factor should be

Question 13: Rationalize the denominator and simplify

(i)

(ii)

(iii)

(iv)

(v)

Question 14: Simplify

(i)

(ii)

(iii)

(iv)

(v)

Question 15: Determine rational numbers and

(i)

and

(ii)

and

(iii)

Let’s first simplify

Now comparing,

Question 16: If and , find

Answer:

Question 17: If and , find

Answer:

Question 18: If , find the value of

Answer:

Therefore

Hence

Question 19: If , find the value of

Answer:

Therefore

Hence

Question 20: If and , find the value of

Answer:

Question 21: If , find the value of

Answer:

Question 22: Given and , find

(i)

(ii)

(iii)

Question 23: Rationalize and simplify:

(i)

(ii)

(iii)