Simplify Square Root Expression: (√12 × √4 × √3)/(√2 × √2)

While you could simplify each radical individually, it's much easier to multiply first! Combining $\sqrt{12} \cdot \sqrt{4} \cdot \sqrt{3} = \sqrt{144}$ gives you a perfect square that's simple to work with.

Look for numbers that are squares of integers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, etc. Since $12^2 = 144$, we know $\sqrt{144} = 12$.

Always look for opportunities to simplify first! In this problem, $\sqrt{2} \cdot \sqrt{2} = \sqrt{4} = 2$, which makes the division much easier than working with radicals in the denominator.

Yes! You could write this as $\sqrt{\frac{12 \times 4 \times 3}{2 \times 2}} = \sqrt{\frac{144}{4}} = \sqrt{36} = 6$. Both methods give the same answer!

Double-check your arithmetic! Common errors include: miscalculating $12 \times 4 \times 3$, forgetting that $\sqrt{2} \times \sqrt{2} = 2$, or making division mistakes.