Here we have:
[tex] \sqrt{{12x^6}y^{12}} [/tex]
factorising 12, we have 12=2*2*3
√12= 2√3 .............(1)
factorising x⁶, we have x⁶ = x*x*x*x*x*x
√x⁶ = x³............(2)
factorising y¹², we have y¹² = y*y*y*y*y*y*y*y*y*y*y*y
√y¹² = y⁶...............(3)
combining (1), (2) and (3) , we have
[tex] \sqrt{{12x^6}y^{12}} [/tex] = 2x³y⁶√3
