Respuesta :

Edufirst
Answer:

[tex] \frac{3}{5} m^2 |n|^{3} [/tex]


1) given

[tex] \sqrt{ \frac{225}{625}m^4n^6 } [/tex]

2) factor 225 and 625

[tex]225=15^2 625=25^2 \sqrt{ \frac{15^2}{25^2}m^4n^6 } [/tex]

3) extract the factors from the radical dividing the exponents by the index of the radical

2/2 = 1 => exponent = 1 =>      [tex] \frac{15}{25} [/tex]

4/2 = 2 => exponent = 2 =>      [tex] m^{2} [/tex] 

6/2 = 3 => exponent = 3=>       [tex] n^{3} [/tex]


[tex] \frac{15}{25} m^2n^3[/tex]

4) simplify the fraction 15/25 = 3/5

=>

[tex] \frac{3}{5} m^2n^3[/tex]

and  you add the absolute symbols | | because it can only be positive.

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