What Is a Square Root? (Mathematics Lesson)
What Is Square Root?A square root is the number which when multiplied by itself gives you the original number.
It is denoted by √.
For example, 6 is the square root of 36, or √36 = 6. This is because 6, multiplied by itself, gives you 36, the original number:
Square Roots and Square NumbersA square root is the inverse of a square number. In other words, taking a square root is the opposite of finding a square number:
How to Find the Square Root of a NumberIt is very difficult to find the square root of a number by hand. It is best to use a calculator.
However, it is simple to find the square root of a square number, since it is the inverse:
NoteWHY "SQUARE" ROOTS?
A square root is the inverse of a square number.
If a number represented the area of a square, then the square root represents the length of the side of that square.
A square with an area of 1 has sides of length 1.
A square with an area of 4 has sides of length 2.
A square with an area of 9 has sides of length 3.
'GUESS-TIMATING' SQUARE ROOTS
It is very difficult to work out a square root without a calculator. But, it is possible to have a good guess from the ones we do know.
The ones we know are the square roots of the square numbers:
1² = 1 so √1 = 1
2² = 4 so √4 = 2
3² = 9 so √9 = 3
4² = 16 so √16 = 4
What is √5?
5 is between 4 and 9.
We can therefore say √5 must be between √4 and √9, or between 2 and 3.