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Sqaure Roots

Theory & Practice Question.

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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