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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 51/3- 5-1/3.

     51/3- 5-1/3=  51/3-

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 .

 

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