Question

Simplify sqrt 10a x sqrt 30a

Answer 1

$\bf \sqrt{10a}\times \sqrt{30a}\implies \sqrt{10a\times 30a}\implies \sqrt{10\cdot 30\cdot a\cdot a}\implies \sqrt{300a^2} \\\\\\ \begin{cases} 300=2\cdot 2\cdot 3\cdot 5\cdot 5\\ \qquad 2^2\cdot 3\cdot 5^2\\ \qquad (2\cdot 5)^2\cdot 3\\ \qquad 10^2\cdot 3 \end{cases}\implies \sqrt{10^2\cdot 3\cdot a^2}\implies 10a\sqrt{3}$