Surds (Cambridge O Level Maths)

Rationalise the denominator.

Rationalise the denominator of .

Expand and simplify .

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

Martin did this question.

Rationalise the denominator of

Here is how he answered the question.

Martin's answer is wrong.

Find Martin's mistake.

Sian did this question.

Rationalise the denominator of

Here is how she answered the question.

Sian's answer is wrong.

Find Sian's mistake.

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.

Rationalise the denominator of 

Show each stage of your working.

Give your answer in the form  where  and  are fractions in their simplest forms.

Given that  is a prime number,

express  in the form  where ,  and are integers.

Without using a calculator, rationalise the denominator of 
Simplify your answer.
You must show each stage of your working.

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

Show your working clearly.

Express  in the form 

where and are integers.
Show your working clearly.

Show that  can be written in the form .

Show that  simplifies to an integer.

Show that    simplifies to an integer.

Rationalise the denominator.

Give your answer in its simplest form.

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

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

Show that      can be written as  

can be written in the form 

Find the value of
Show your working clearly.

Rationalise the denominator of  where  is an integer and is a prime number.

Simplify your answer.

Show that  can be written in the form 

where and are integers.
Show your working clearly.

Express  in the form  where a and b are integers.

Show each stage of your working clearly.

The area of a rectangle is

The length of the rectangle is .

Without using a calculator and showing each stage of your working, find the width of the rectangle.

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

.....................

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

Show each stage of your working clearly and give the value of a and the value of .

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

Find when  = 7.

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

Find when = 64.

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

 Show that  can be simplified to 

Here is a sequence.

      5        15   

Work out the next term.

Find the th term.

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.