Surds (AQA GCSE Maths: Higher): Exam Questions

Rationalise the denominator of  .

Work out the value of  .

Work out the value of        .

Rationalise the denominator of    .
Give your answer in its simplest form.

Work out       

Give your answer as an integer.

Rationalise the denominator and simplify 

Circle the number that is closest in value to 

 Show that   can be written in the form  where and are integers.

Show that 

can be written in the form where is a simplified fraction and is an integer.

Show that 

Show each stage of your working.

Show that can be expressed in the form  where is an integer.

Show your working clearly.

Show that
Show your working clearly.

Rationalise the denominator of

Give your answer in its simplest form.

Without using a calculator, show that .

Write     in the form  .

Simplify .

Simplify fully by rationalising the denominator.

Simplify fully.

Write  in the form .

Simplify fully.

.

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.