Week 3 – Math 11 – Variable Radicands

As we have just finished our Roots and Powers unit, we are now moving onto the next which seems to be all about square roots. Our first lesson on it was pretty confusing, so I had to do some research on what we learned my own time.

The main new concept I learned was variable radicands and converting them into mixed radicals. I can’t really think of how to explain with just words, so I will go straight into the examples and I’ll explain as I go.

Lets use $\sqrt {75a^2}$ as our first example.

What we would do first is to factor our number to separate perfect squares from imperfect squares (if we can).

I’ll explain what I’m doing in brackets.

$\sqrt {75a^2} = \sqrt {25 \times 3 \times a^2}$ (factor)

$= \sqrt {25} \times \sqrt {3} \times \sqrt {a^2}$ (separate to make things easier)

After this, all we need to to is simplify.

$= 5a \sqrt {3}$ (simplify)

Let’s do another example to get the hang of this. This time I’ll use $\sqrt {18b^5}$

This one will be slightly different because our variable has an exponent that will make things difficult. Although it’s more difficult, we still do the same steps.

$\sqrt {18b^5} = \sqrt {18 \times b^5}$ (factor)