## Square Root Calculator

## 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:

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

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

- Try a number – 5 : 5 times 5 = 25 (too low)
- Try a number that is more than 6 – 10 – 10 times 10 = 100 (too high
- 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

## Square root number table – imperfect squares

## Sources and more resources

- An introduction to square roots from Wolfram MathWorld and Wikipedia.
- A video introduction to square roots from Khan Academy and Math Planet.
- How to quickly find a square root from tecmath
- How to manually find a square root by John Kerl and HomeSchoolMath.net.