3.1.8 Square Root Problems

A common question involves the multiplication of two square roots together to solve for (usually) an integer value. For example:

$$\sqrt{12} \times \sqrt{27} = \sqrt{12} \times \sqrt{3} \times \sqrt{9}$$ $$= \sqrt{36} \times \sqrt{9}$$ $$= 6 \times 3 = 18$$

Usually the best approach is to figure out what you can take away from one square roots and multiply the other one by it. So from the above example, notice that we can take a 3 away from 27 to multiply the 12 with, leading to just $\sqrt{36} \times \sqrt{9}$ which are easy square roots to calculate. With this method, there are really no “tricks” involved, just a method that should be practiced in order to master it. The following are some more problems:

Problem Set 3.1.8