Squares, roots and powers
Squares, roots and powers

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Squares, roots and powers

1.1.1 Try some yourself

Activity 1

Evaluate the following:

  • (a) 62

  • (b) 0.52

  • (c) 1.52

Answer

  • (a) 62 = 6 × 6 = 36

  • (b) 0.52 = 0.5 × 0.5 = 0.25

  • (c) 1.52 = 1.5 × 1.5 = 2.25

Activity 2

Square carpet tiles measure 50 cm by 50 cm (or 0.5 m by 0.5 m).

  • (a) What area is covered by one tile? Give your answer (i) in square centimetres (cm2) and (ii) in square metres (m2).

  • (b) What area, in m2, will 100 tiles cover?

  • (c) How many tiles are needed to cover 1 square metre?

  • (d) How many tiles are needed to cover a room with an area of 16 m2?

  • (e) If the room in (d) is square, how many tiles go along each edge?

Answer

  • (a)(i) One tile covers 50 × 50 = 2500 cm2.

  • (a)(ii) To convert this to m2, you could divide by 1002 to give = 0.25 m2.

  • Alternatively (and more simply) convert first: each tile measures

  • 0.5 m × 0.5 m and so has an area 0.5 m × 0.5 m = 0.25 m2.

  • (b) One tile covers 0.25 m2 so 100 tiles cover 100 × 0.25 = 25 m2.

  • (c) Since each tile covers 0.25 m2, 4 tiles will cover 4 × 0.25 = 1 m2.

  • (d) 4 tiles cover 1 m2 so 16 × 4 = 64 tiles cover 16 m2.

  • (e) If the room is square and the area is 16 m2 then each edge must be 4 m, since 4 × 4 = 16 (or =4). So 8 tiles go along each edge.

  • (You could also have deduced this from your answer to (d), since 64 tiles is 8 × 8 tiles.)

MU120_4M4

For further information, take a look at our frequently asked questions which may give you the support you need.

Have a question?
Free Courses

OpenLearn has over 800 free courses across all our subjects designed by our academic experts. From 1 to 100 hours, introductory to advanced, you can start learning at any time and all for free.