Simplify The Equation Below

Question

anonymous · Answer

$$4\sqrt{4} \over \sqrt{7}$$

mathmate · Answer

Mathematicians do not like seeing square roots in the denominators, because they make addition and subtraction of fractions messy.
The process to remove them (and keep the same value of the expression) is called rationalizing the denominator.
In this case, we only have to multiply top and bottom by sqrt(7):
$$\frac{4\sqrt4}{\sqrt7}\frac{\sqrt7}{\sqrt7}$$
$$=\frac{4\sqrt4\sqrt7}{7}$$
$$=\frac{4\sqrt{28}}{7}$$
That's about all we can do to simplify the expression.

anonymous · Answer

wow, so easy!

anonymous · Answer

Thanks Man! @mathmate

mathmate · Answer

You're welcome!  ::)

e.mccormick · Answer

Nope.  $2=\sqrt{4}$ so you can take that out from under the root to start.

e.mccormick · Answer

Simplifying roots is an exercise in prime factoring and removing sets.

mathmate · Answer

Thank you @e.mccormick  I was preoccupied and overlooked it.
Thank you so much.

e.mccormick · Answer

Yah, happens.  Hehe.  I told someone stuff about area of a triangle because of a graph... and it was supposed to be area of a rectangle inscribed in the triangle!  We all miss things at times.

mathmate · Answer

Yep! Totally agree!  Happens to everyone!

e.mccormick · Answer

$\dfrac{4\sqrt4}{\sqrt7}\cdot\dfrac{\sqrt7}{\sqrt7}\implies \dfrac{4\sqrt{2\cdot 2\cdot 7}}{\sqrt{7\cdot 7}}\implies \dfrac{4\cdot 2\sqrt7}{7}$

so in the end:

$\dfrac{8\sqrt7}{7}$

mathmate · Answer

Yep, perfect!

e.mccormick · Answer

Yah, explains what I meant by prime factors being the key to reducing roots.

mathmate · Answer

@AjMJackKnife  please check correction!