Question

Simplify the expression please with step

`\sqrt{13 - 4 √(3) }`
​

Answer 1

`\huge \boxed{ \boxed{ \red{2 √(3) - 1}}}`

Explanation:

to understand this

you need to know about:

• redical
• simplifying redical
• PEMDAS

given:

• 
  `\tt \sqrt{13-4√(3)}`

to do:

• simplification

tips and formulas:

1. (a-b)²=a²-2ab+b²
2. √(a)²<=>|a|

let's do:

`\tt \sqrt{13 - 4 √(3) }`

`step - 2 : simplify`

1. 
   `\tt use \: the \: 1 \: formula : \\ \tt \sqrt{ 1 + 12 - 4 √(3) } \\ \tt \sqrt{1 - 4 √(3) + 12} \\ \tt \sqrt{ {(1)}^(2) - 2.1.2 √(3) + {(2 √(3)) }^(2) } \\ \sqrt{ \tt (1 - 2√(3) {)}^(2) }`
2. 
   `\tt use \: the \: 2 \: formula : \\ \tt |1 - 2√(3) | \\ \tt - (1 - 2 √(3) ) \\ - 1 + 2 √(3) \\ 2 √(3) - 1`