Square Root Problems

A common question involves the multiplication of two square roots together to solve for an integer value. The best approach is to factor the numbers under the radicals to find perfect squares that can be simplified.

For example, $\sqrt{12} \times \sqrt{27}$ can be simplified by 'moving' a factor of 3 from 27 to 12. This turns the problem into $\sqrt{12 \times 3} \times \sqrt{9} = \sqrt{36} \times \sqrt{9} = 6 \times 3 = 18$. This method avoids dealing with larger numbers under the radical and is a matter of practice to master.