1. Express as a pure surd.

a) 5√6 b) c) 

a)

b)

c)

2.Which is greater either .

3. Express as a mixed surd in its simplest form.

          1.√80   2. 3.

4. Arrange  in ascending order of magnitude and hence write them in descending order of magnitude.

Ascending order:

Descending order:

5.Simplify  .

6. Simplify .

7. Simplify  and express the result in its simplest form.

8. Simplify  x √5 and express the result in its simplest form.

9. write the simplest rationalising factor of 

a. 3√3  b.

 a. 3√3 x √3 = 3x3=9 

Therefore  √3 is the rationalising factor.

b.√108 = =6√3 

 6√3 x √3=6x3 = 18.

 Therefore √3 is the rationalising factor.

10.Express the following surds with rational denominators.

11. Given that √2=1.414 and √3=1.732.Find.

 12.If x = 2√6 + 5. Find .

 Given x = 2√6 + 5

13.Rationalise 5^1/3- 5^-1/3.

     5^1/3- 5^-1/3=  5^1/3-

This is in the form (a-b)

Therefore Rationalising factor will be a²+ab+b².

 Therefore Rationalising factor =

14.Rationalise the denominator of .

15.Rationalise the numerator of .

 .

16.If ; a and b are rational numbers, find the value of a and b.

      Given that 

17.Simplify .

18. Simplify .

19. Simplify .

20. Simplify .