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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 Numbers

A 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 Number

It 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:

Quick Test
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Note
WHY "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.