Surds (AQA GCSE Further Maths)

Rationalise and simplify 

Give your answer in the form  where and  are integers.

Rationalise the denominator and simplify fully    

Solve   

Solve

giving your answer in the form

where and are integers to be found.

Work out the value of .

is a triangle.

The perpendicular from meets at .

Area of triangle

Work out the length, in cm, of .

Give your answer in the form where and are integers.

........................cm

Rationalise the denominator and simplify fully

Give your answer in the form where is a prime number which you should find.

You are given that where and are positive integers.

Find and .