The square area is calculated by the length of the page x the length of the page. If the length of the page is 2 meters, then the square area is [math]2\, m \cdot 2\, m = (2\,m)^2 = 4\, m^2.[/math] If we happen to know the square area, then with the square root we can find out the length of the page:[br] [br][math] \sqrt{4\;m^2} = \sqrt{(2\,m)^2} = 2\,m.[/math][br] [br][color=#0000ff]The square root tells you which number, when raised to another power, gives that result. [/color] Square root is denoted [math] \sqrt{}[/math] or less often [math] \sqrt[2]{}[/math]

[br]Mathematical definition for a square root is: [br][br][color=#0000ff]Let [math]\large \textcolor{blue}{x\geq 0.}[/math] The [i][b]square root of [/b][/i][b]x[/b] means the real number, for which[/color][br] [br]  [math]\large \textcolor{blue}{\sqrt x \geq 0 \;\;\text{ and }\;\; (\sqrt x)^2=x.}[/math][br] [br]This means that the result of the square root is at least 0 and the result, when raised to another, gives the result of [i]x[/i]. Examples 4 and 5 note that the [color=#0000ff] addition and subtraction within the square root must always be performed before the square root is taken [/color]. The square root of the multiplication and division can be taken separately (see examples 5 and 6).[br] [br][br][br] 1.  [math] \sqrt 4=\sqrt{2^2}=2, \text{ sillä } 2^2=4[/math][br] [br] 2.  [math] \sqrt{(-2)^2}=\sqrt 4=2= |-2|. [/math][br] [br]The original number -2 cannot be given here, as the value of the square root must always be at least 0. If you are not sure of the sign of the number, then you should use absolute values. For example[br][br] 3. [math]\sqrt{a^2}=|a|[/math][br][br]because we don't know if [i]a[/i] represents a positive or negative number. Absolute value signs ensure that the result is positive.[br][br] 4. [math] \sqrt{16+9}=\sqrt{25}=5[/math][br][br]The square root cannot be taken separately from the terms of the sum, i.e. the sum (= addition or subtraction) must be calculated first.[br][br] 5.  [math] \sqrt{2^2+6^2}=\sqrt{4+36}=\sqrt{40} =\sqrt{4\cdot 10}=\sqrt 4\cdot \sqrt{10}=2\sqrt{10}[/math][br][br]In this calculation, the answer [math]\sqrt{40}[/math] is just as correct as [math]2\sqrt{10}. [/math] Quite often, the latter form is used in solving tasks, although "it looks mathematically more beautiful". There is no need to take pressure from this, because it is more important to know how to calculate correctly.[br] [br] 6.  [math]\sqrt\frac 4 9=\frac \sqrt 4 \sqrt 9=\frac 2 3 [/math][br][br][br][br][br][br]