[tex] \sqrt{5} \times \sqrt[4]{5} [/tex]​

Answer:   " 3.344 " .________________________________________Step-by-step explanation:_______________________________________Note:  √5  =  [tex]5^{(1/2)}[/tex]  .  →  {Since:  [tex]\sqrt{5} = \sqrt[2]{(5^1)}  = \sqrt[2]{5}[/tex] } ;        and note the following property of "roots" :_______________________________________               →   [tex]\sqrt[n]{x^y}  =   x^{(y/n)}[/tex]  ' _______________________________________       [tex]\sqrt[4]{5} = 5^{(1/4)}[/tex] ._______________________________________     →   [tex]\sqrt{5}  * \sqrt[4]{5}[/tex]   ;        =  [tex]5^{(1/2)}[/tex]  * 5^{(1/4) ;        =    [tex]5^{[(1/2) +(1/4)]}[/tex] ;_______________________________________Note:  Refer to the following property of exponents:           →    xᵃ  * xᵇ =  x⁽ᵃ ⁺ ᵇ⁾_______________________________________Now, (1/2) + (1/4) = ? ;  Note:  (1/2) = (?/4)  ?? ;  →  Look at the "denominators" ;      2 * ? = 4  ? '         →  4 ÷ 2 = ? ;         →  4 ÷ 2 = 2 .  →  So:  2 * 2 = 4; ; →  Now, look at the "numerators" ;           1 * 2 = 2 ; So,  (1/2) = (2/4) ; →  (1/2) + (1/4) = (2/4) + (1/4) =  (2 + 1) / 4 =  3/4 ._______________________________________So:   [tex]5^{[(1/2) +(1/4)]}[/tex] ;            =  [tex]5^{3/4)]}[/tex] ;          =  3.34370152488  ; (using calculator) ;              → round to:  " 3.344 ". ________________________________________