\(\sqrt{a} \times \sqrt{a} = a\)

\(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)

\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)

Simplify \(\sqrt{12}\).

4 is a factor of 12 so we can write \(\sqrt{12} = \sqrt{(4\times3)} = \sqrt{4}\times\sqrt{3}\)

\(\sqrt{4} = 2\) so \(\sqrt{12} = 2\sqrt{3}\)

Simplify \(\sqrt{10} \times \sqrt{5}\)

\(\sqrt{10} \times \sqrt{5} = \sqrt{50}\)

\(50 = 25 \times 2\), so we can write \(\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}\)

Simplify \(\frac{\sqrt{12}}{\sqrt{6}}\)

\(\frac{\sqrt{12}}{\sqrt{6}} = \sqrt{\frac{12}{6}} = \sqrt{2}\)