Mathematics
Squares and square roots
Class 7
Intermediate
About 15 min
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Squares and square roots: buying a square carpet
Choose the area of a square carpet and find how long its sides are; estimate square roots that are not whole numbers.
Core concept
The side of a square is the square root of its area; a square root lies between the roots of the nearest perfect squares
Topic: Squares and square roots
A family wants a square carpet that covers 49 m² of floor. How long is each side? A square with side s has area: How much flat space a shape covers, measured in square units like cm². All key words s × s = s², so the side is the number that squares to the area: the square root, √49 = 7 m. Areas like 1, 4, 9, 16, 25, … are perfect squares and have whole-number roots. Other areas, like 50 m², have roots that are not whole: √50 lies between √49 = 7 and √64 = 8, a little above 7.
What you will learn
- Find the square of a number and the square root of a perfect square.
- Estimate a square root between two whole numbers.
- Use square roots to find the side of a square from its area.
Before you start
- Multiplication tables up to 12 × 12; area of a square.
Materials
- Square paper tiles
Equipment
- A measuring tape
Procedure
- Drag the corner of the carpet to change its area.
- Read the side, √area, and see the grid of whole square metres.
- For areas that are not perfect squares, read the number line between the nearest whole numbers.
- Record carpets of 64 m², 50 m², 2 m² and 144 m².
How this simulation is simplified
- The carpet is an exact square.