Squares and Square Roots
1.0 Numbers · 1.4 Squares and Square Roots
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.4 Squares and Square Roots (6 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Work out the squares of numbers from tables and using a calculator
- Work out the square roots of numbers from tables and using a calculator
- Enjoy using squares and square roots in real-life situations
Squares and Square Roots
A square tile measuring 7 cm on every side covers 49 cm². That is where the word comes from. Squaring a number gives the area of a square with that side.
a) Squaring a number
To square a number, multiply it by itself.
We write it with a small 2 above and to the right. Say 7² as "seven squared".
Be careful: 7² is 49, not 14. Squaring is not the same as doubling.
Squaring a decimal smaller than 1 gives an answer smaller than the number you started with. That looks wrong but it is correct, because you are taking a part of a part.
b) Why it is called squaring
A square with side 7 cm has area 7 × 7 = 49 cm². The picture and the arithmetic are the same thing.
c) Perfect squares
Some numbers come from squaring a whole number. These are perfect squares.
| Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Square | 1 | 4 | 9 | 16 | 25 | 36 | 49 | 64 | 81 | 100 |
Learning these ten saves time in almost every topic that follows.
Notice the gaps between them grow: 1, 4, 9, 16 rise by 3, then 5, then 7. The squares never bunch together.
d) Square roots
Finding a square root is the reverse of squaring. It asks which number, multiplied by itself, gives the number you have.
The symbol is √. So √49 = 7, because 7 × 7 = 49.
Every perfect square in the table above has a whole number square root. Reading the table backwards gives you those roots for free.
e) Using tables and a calculator
Not every number is a perfect square. √2 is not a whole number and never becomes one, no matter how far you go.
For these, use mathematical tables or the √ key on a calculator.
Estimate first. √50 must lie between 7 and 8, because 7² is 49 and 8² is 64. If the calculator shows 70, a key has been pressed wrongly.
Check by squaring back. Multiply your answer by itself. You should return to roughly the number you started with.
f) Reading four-figure tables
Find the row for the whole part and the column for the first decimal place. Read the value where they meet, then add the small correction from the difference columns on the right.
Tables give four figures, so answers are approximate. A calculator gives more figures but is still rounding somewhere.
g) Where this is used
A builder works out how many tiles cover a square floor. A carpenter finds the side of a square table from its area. Anyone using Pythagoras' theorem squares and roots numbers constantly.
Words to know
- Square (of a number) -- the result of multiplying a number by itself, written with a small 2 (e.g. 17²).
- Square root -- the number which, multiplied by itself, gives a target value; the reverse operation of squaring.
:::checkpoint Check yourself
- Work out 9².
- What is √81?
- Between which two whole numbers does √30 lie?
- Why is 0.5² smaller than 0.5? :::
Bridge to practice
Try the exercises below -- on finding squares, square roots, and applying them to real-life area problems.