Question

Simplify. square root (108 x^5 y^6)

Answer 1

`\bf √(108x^5y^6)\qquad \begin{cases} 108=2\cdot 2\cdot 3\cdot 3\cdot 3\\ \qquad 2^2\cdot 3^2\cdot 3\\ \qquad (2\cdot 3)^2\cdot 3\\ \qquad 6^2\cdot 3\\ x^5=x^(4+1)\\ \qquad x^4\cdot x^1\\ \qquad x^(2\cdot 2)\cdot x\\ \qquad (x^2)^2\cdot x\\ y^6=y^(3\cdot 2)\\ \qquad (y^3)^2 \end{cases}\implies √(6^2\cdot 3\cdot (x^2)^2\cdot x\cdot (y^3)^2) \\\\\\ 6x^2y^3√(3x)`