# Square Root

LAST UPDATE: October 20th, 2020

## Definition – What is a square root?

The square root of a number is the number that, when multiplied by itself, gives the original number.

For example, the square root of 9 is 3, as 3 x 3 = 9.

The square root of 25 is 5, as 5 x 5 = 25.

The square root of 49 is 7, as 7 x 7 = 49.

The square root can be positive or negative (-3 x -3 equals 9, -5 x -5 = 25, and -7 x -7 = 49). When people say “square root,” they usually refer to the positive square root.

The opposite of a square root is a squared (power of 2) calculation.

## What is square root used for?

From a practical standpoint, in geometry square root can be used to find the length of a side of a square when the area is known.

## Formula – How to calculate the square root of a number

There is no quick mathematical formula to calculate a square root. Most calculators use a form of very fast trial and error.

### Method 1 – Trial and error

Trial and error works well for perfect squares. It can be very time consuming for non-perfect squares as there are many decimal places.

To find a square root by trial and error:

1. Guess a number that you think could be the square root.
2. Multiply that number by itself
3. If the result is too low, try another higher number. If the result is too high, try another lower number.
4. Keep going until you find the square root.

Example – Find the square root of 64 using trial and error:

1. Try a number – 5 : 5 times 5 = 25 (too low)
2. Try a number that is more than 6 – 10 – 10 times 10 = 100 (too high
3. Try a number in between 6 and 10 – 8 – 8 times 8 = 64 (answer)

### Method 2 – Quickly find roots from perfect square numbers

This method makes it quicker to find the root of a perfect square number. If the number is not a perfect root, however, this method won’t work.

### Method 3 – Shortcut to find the square root of any number

This method can find the square root of any number (including non-perfect squares). It takes a bit longer than method 2.

## How do you type square root?

• You can copy the square root symbol -> √ <- from this page and paste it into your document.
• On a windows computer, open the character map, find the square root symbol, and copy it. Paste it where you want the symbol.
• On a mac computer, press option + v for the √ symbol.

## Square root number table – perfect squares

• √1 = 1, as 1 x 1 = 1
• √4 = 2, as 2 x 2 = 4
• √9 = 3, as 3 x 3= 9
• √16 = 4, as 4 x 4 = 16
• √25 = 5, as 5 x 5 = 25
• √36 = 6, as 6 x 6 = 36
• √49 = 7, as 7 x 7 = 49
• √64 = 8, as 8 x 8 = 64
• √81 = 9, as 9 x 9 = 81
• √100 = 10, as 10 x 10 = 100
• √121 = 11, as 11 x 11 = 121
• √144 = 12, as 12 x 12 = 144
• √225 = 15, as 15 x 15 = 225
• √289 = 17, as 17 x 17 = 289
• √400 = 20, as 20 x 20 = 400
• √625 = 25, as 25 x 25 = 625
• √900 = 30, as 30 x 30 = 900
• √1089 = 33, as 33 x 33 = 1,089
• √2025 = 45, as 45 x 45 = 2,025
• √2500 = 50, as 50 x 50 = 2,500
• √3600 = 60, as 60 x 60 = 3,600
• √5625 = 75, as 75 x 75 = 5,625
• √10000 = 100, as 100 x 100 = 10,000