Question

Simplify sqrt 10a x sqrt 30a

Answer 1

`\bf √(10a)* √(30a)\implies √(10a* 30a)\implies √(10\cdot 30\cdot a\cdot a)\implies √(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 √(10^2\cdot 3\cdot a^2)\implies 10a√(3)`