Respuesta :

we are given

[tex] \sqrt{\frac{400}{49}} [/tex]

we can write it as

[tex] =\frac{\sqrt{400}}{\sqrt{49}} [/tex]

now, we can factor top and bottom

[tex] =\frac{\sqrt{20*20}}{\sqrt{7*7}} [/tex]

[tex] =\frac{\sqrt{20^2}}{\sqrt{7^2}} [/tex]

now, we can simplify it

we get

[tex] =\frac{20}{7} [/tex]

now, we can change in mixed form

[tex] =2\frac{6}{7} [/tex]...............Answer

gmany

[tex] \sqrt{\dfrac{400}{49}}=\dfrac{\sqrt{400}}{\sqrt{49}}=\dfrac{20}{7}=2\dfrac{6}{7}\\\\\text{Used}\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\\sqrt{400}=20\ \text{because}\ 20^2=400\\\\\sqrt{49}=7\ \text{because}\ 7^2=49 [/tex]

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