Problem solving with surds

12 questions

1. Order the fractions from smallest to largest.
2. What is the value of a + b - c when a = 7, b = 21 and c = 2.4
3. In order to rationalise (2 - \sqrt {3}) you would multiply by:
4. True or false? Pythagoras' theorem can only be used to find the length of the hypotenuse.
5. When is a surd in it's simplest form?
6. Solve x\sqrt {180} - 30 = x\sqrt {80} and write your answer in the form a\sqrt {b}. State the value of b.
7. True or false? Surds are a way of giving an answer exactly.
8. Arrange the surds from smallest to largest.
9. The perimeter of a rectangle is 12 + 8\sqrt {2}. One of the lengths is 6 + \sqrt {2}. Find the area.
10. The length of the line between (3,8) and (7,13) can be written in the form \sqrt {a}. What is the value of a?
11. Which of these shapes has a greater area?
12. Which of these shapes has a greater perimeter?

License: OGL