Question

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

Answer 1

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