Question

I'm very confused on what to do :/

Answer 1

$\sqrt{99w^5m^3}$

$\sqrt{99} \sqrt{w^5m^3}$

$\sqrt{99}=3\sqrt{11}$

$=3\sqrt{11}\sqrt{w^5m^3}$

Hope this helps!

Thanks!

-Charlie

Answer 2

To simplify a term under a square root, we are going to try and find factors of the term that are to a power of 2. This is because when there is a term under a square root that is being squared, the powers cancel out and we are left with the term itself. An example of this is:

$\sqrt{8x^4} = \sqrt{2^2 \cdot 2 \cdot x^2 \cdot x^2} = 2x^2\sqrt{2}$

So, we will first look at the 99. Are there any factors of 99 that are a whole number squared? Sure! 9 is equal to $3^2$. Thus, we can say that 99 simplifies as follows:

$99 = 11 \cdot 3^2$

(Remember that the 11 comes from the fact that 11 times 9 is equal to 99. We can't have a 3^2 without the 11!)

Now, let's look at the $w^5$. Remember that exponents of the same base add to each other. Thus, we can say:

$w^5 = w^2 \cdot w^2 \cdot w$

Now, let's examine the $m^3$. Again, using the fact that exponents add, we can say:

$m^3 = m \cdot m^2$

Now, let's substitute all of this back under the square root to get:

$\sqrt{(11 \cdot 3^2) \cdot (w^2 \cdot w^2 \cdot w) \cdot (m^2 \cdot m)}$

The next step is to take out the terms to the power of 2. This gets us:

$3 \cdot w \cdot w \cdot m \sqrt{11 \cdot w \cdot m}$

$3w^2 m \sqrt{11wm}$

Our answer is $\boxed{3w^2 m \sqrt{11wm}}$.