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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