Table of Contents
How to Square A Number
To square a number:
Multiply the number by itself.
What is 4 squared?
4 squared = 4 × 4 = 16
“Squared” is often written as a little 2 like this:
42 = 16
This says “4 Squared equals 16“
(the little 2 says the number appears twice in multiplying)
Perfect Squares
The Perfect Squares (also called “Square Numbers“) are the squares of the integers:
Perfect Squares From 02 to 102
Number | Square |
0 | 0 |
1 | 1 |
2 | 4 |
3 | 9 |
4 | 16 |
5 | 25 |
6 | 36 |
7 | 49 |
8 | 64 |
9 | 81 |
10 | 100 |
Negative Numbers
We can also square negative numbers.
What happens when we square (−7) ?
Answer:
(−7) × (−7) = 49
(because a negative times a negative gives a positive)
When we square a negative number we get a positive result.
Square Roots
A square root goes the other way:
What can we multiply by itself to get this?
Find a square root of 25
What can we multiply by itself to get 25?
A square root of 25 is 5, because when 5 is multiplied by itself we get 25.
So,
a square root of a number is a value that can be multiplied by itself to give the original number.
Negatives Roots
We discovered earlier that we can square negative numbers:
(−6) squared
(−6) × (−6) = 36
And of course 6 × 6 = 36 too.
So the square root of 36 could be −6 or +6
Perfect Square Roots
The Perfect roots are the roots of the integers:
Square | Square Root |
1 | 1 or -1 |
4 | 2 or -2 |
9 | 3 or -3 |
16 | 4 or -4 |
25 | 5 or -5 |
36 | 6 or -6 |
49 | 7 or -7 |
64 | 8 or -8 |
81 | 9 or -9 |
100 | 10 or -10 |
The Square Root Symbol
√
This is the special symbol that means “square root“.
Use it like this:
√49 is 7
we say “square root of 49 equals 7”
What is √81 ?
81 = 9 × 9
in other words when we multiply 9 by itself (9 × 9) we get 81
So the answer is:
√81 = 9
Square Root Day
The April 4th 2016 is a Square Root Day, because the date looks like 4/4/16
The next after that is the May 5th 2025 (5/5/25)