Surds (AQA GCSE Maths: Higher): Exam Questions

Rationalise the denominator of .

Expand and simplify .

Expand   
Give your answer in the form  where and are integers.

Simplify fully 

You must show your working.

    can be written in the form  where is an integer.

Find the value of .

Show that    simplifies to  .

Express   in the form  where  is an integer.

Express  in the form  where  and  are integers.

Show that    simplifies to an integer.

Show that  simplifies to an integer.

Work out the value of .
Give your answer in the form  where is an integer.

Simplify 

Give your answer in the form      where and are integers.

Work out    

Give your answer in the form   where and are integers.

Show that  can be written in the form 

where and  are integers.

can be written in the form 

Find the value of Show your working clearly.

In the following equation, is an integer greater than 1.

i) Find when  = 7.

= ...................... [2]

ii) Find when = 64.

= ..................... [2]

Here is a sequence.

      5        15   

Work out the next term.

Find the th term.