## Theory

##### Square Root

The square root of a given number is the positive number that, when multiplied by itself, produces the given number.

Below is a list of common square root

Square root form | √1 | √4 | √9 | √16 | √25 | √36 | √49 | √64 | √81 | √100 | √121 | √144 |

Basic numeral | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

The cube root of a given number is the number that, when multiplied by itself twice, produces the given number

## Example

Which two integers does √132 lie between?

## Solution

Find the largest square less than 132 and smallest square greater than 132.

The largest square less than 132 is 11

√121 = 11

The smallest square greater than 132 is 12

√144 = 12

## Question

Between which two whole numbers is √2

## Explanation

We need to select two whole numbers, for which our root sits inbetween, such that these two numbers have a square root. We know that

1 < 2 < 4

Rooting everything gives

1 < √2 < 2

√2 is between 1 and 2

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