Square Root Cheat Sheet (customizable)

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[See also Square Cheat Sheet]

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Square Root of a Number (√x)

√	=	1.00
√	=	1.41
√	=	1.73
√	=	2.00
√	=	2.24
√	=	2.45
√	=	2.65
√	=	2.83
√	=	3.00
√	=	3.16
√	=	3.32
√	=	3.46
√	=	3.61
√	=	3.74
√	=	3.87
√	=	4.00
√	=	4.12
√	=	4.24
√	=	4.36
√	=	4.47
√	=	4.58
√	=	4.69
√	=	4.80
√	=	4.90
√	=	5.00

√	=	5.10
√	=	5.20
√	=	5.29
√	=	5.39
√	=	5.48
√	=	5.57
√	=	5.66
√	=	5.74
√	=	5.83
√	=	5.92
√	=	6.00
√	=	6.08
√	=	6.16
√	=	6.24
√	=	6.32
√	=	6.40
√	=	6.48
√	=	6.56
√	=	6.63
√	=	6.71
√	=	6.78
√	=	6.86
√	=	6.93
√	=	7.00
√	=	7.07

√	=	7.14
√	=	7.21
√	=	7.28
√	=	7.35
√	=	7.42
√	=	7.48
√	=	7.55
√	=	7.62
√	=	7.68
√	=	7.75
√	=	7.81
√	=	7.87
√	=	7.94
√	=	8.00
√	=	8.06
√	=	8.12
√	=	8.19
√	=	8.25
√	=	8.31
√	=	8.37
√	=	8.43
√	=	8.49
√	=	8.54
√	=	8.60
√	=	8.66

√	=	8.72
√	=	8.77
√	=	8.83
√	=	8.89
√	=	8.94
√	=	9.00
√	=	9.06
√	=	9.11
√	=	9.17
√	=	9.22
√	=	9.27
√	=	9.33
√	=	9.38
√	=	9.43
√	=	9.49
√	=	9.54
√	=	9.59
√	=	9.64
√	=	9.70
√	=	9.75
√	=	9.80
√	=	9.85
√	=	9.90
√	=	9.95
√	=	10.00

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Exporting the Cheat Sheet to PDF

To export the cheat sheet as a PDF, you can follow these simple steps that leverage the browser's capabilities to save the printer-friendly version of the sheet as a PDF:

Click on the Printer friendly link (here or above the table), or on the Worksheet link if you wanted to get the Worksheet instead of the Cheat Sheet.
Press Ctrl + P (or Cmd + P on Mac) to open the print dialog
In the print dialog, choose Save as PDF as the destination.

The specific steps may vary slightly depending on the browser being used. This enables you to create a portable and accessible version of the cheat sheet that you can refer to anytime, anywhere.

What is the square root of a number?

The square root of a number x is a value y such that y² = x. In other words, when you multiply y by itself, you get x. Mathematically, this is expressed as:

y = √x

For example:

The square root of 16 is 4 because 4 × 4 = 16
The square root of 25 is 5 because 5 × 5 = 25

Every positive number has two square roots: a positive and a negative one. For instance, both 4 and -4 are square roots of 16 because 4² = 16 and -4² = 16. The principal square root (the non-negative one) is usually what is referred to when we say the square root.

It is worth noting that the square root of a number is not always an integer; in many cases, it is a non-integer (a floating-point number). When the square root of a number is not a perfect square (i.e., an integer squared), the result will be a floating-point number.

For example:

The square root of 2 is approximately 1.414 because 1.414² ≈ 2.
The square root of 3 is approximately 1.732 because 1.732² ≈ 3.
The square root of 5 is approximately 2.236 because 2.236² ≈ 5.

In these cases, the square root cannot be expressed as an exact integer. Instead, it is a non-repeating, non-terminating decimal (an irrational number). Calculators and computer algorithms typically approximate these values to a certain number of decimal places for practical use.

When dealing with floating-point numbers, precision is limited by the number of decimal places, but mathematically, the square root of non-perfect squares is always irrational, meaning it cannot be precisely written as a simple fraction or integer.