Respuesta :

Answer:

[tex] \huge \boxed{ \boxed{ \red{2 \sqrt{3} - 1}}}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • redical
  • simplifying redical
  • PEMDAS

given:

  • [tex]\tt \sqrt{13-4\sqrt{3}}[/tex]

to do:

  • simplification

tips and formulas:

  1. (a-b)²=a²-2ab+b²
  2. √(a)²<=>|a|

let's do:

[tex]step - 1 : define [/tex]

[tex] \tt \sqrt{13 - 4 \sqrt{3} } [/tex]

[tex]step - 2 : simplify[/tex]

  1. [tex] \tt use \: the \: 1 \: formula : \\ \tt \sqrt{ 1 + 12 - 4 \sqrt{3} } \\ \tt \sqrt{1 - 4 \sqrt{3} + 12} \\ \tt \sqrt{ {(1)}^{2} - 2.1.2 \sqrt{3} + {(2 \sqrt{3}) }^{2} } \\ \sqrt{ \tt (1 - 2\sqrt{3} {)}^{2} } [/tex]
  2. [tex] \tt use \: the \: 2 \: formula : \\ \tt |1 - 2\sqrt{3} | \\ \tt - (1 - 2 \sqrt{3} ) \\ - 1 + 2 \sqrt{3} \\ 2 \sqrt{3} - 1[/tex]