Question

`x^3√(175x^7y^5)`

Answer 1

`5x^(6)y^(2) √(7xy)`

Explanation:

Fistly , you have to know these :

`a√(x) + b√(x) = (a+b)√(x) \\\sqrt{a.b^(2) } =b√(a) \\ c\sqrt{a.b^(2) } =(c.b)√(a) \\a√(x) - b√(x) = (a-b)√(x)`

About your question:

`x^(3)\sqrt{175x^(7)y^(5)}`

`x^(3)\sqrt{175x^(2).x^(2).x^(2).x.y^(2).y^(2).y}`

`√(175) =√(25.7) = 5√(7)`

`5x^(3)\sqrt{7.x^(2).x^(2).x^(2).x.y^(2).y^(2).y}`

`5x^(3).x.x.x\sqrt{7.x.y^(2).y^(2).y}`

`5x^(6)\sqrt{7.x.y^(2).y^(2).y}`

`5x^(6).y.y√(7.x.y)`

`5x^(6).y^(2)√(7.x.y)`

=>
`5x^(6)y^(2) √(7xy)`<=

Hope it helps ^-^