# gahh help

##### New member
ok the question is
sqrt 4/ sqrt 27
then i got
sqrt 108/ 27

then what?

help me!! gracias

#### Denis

##### Senior Member
ok the question is
sqrt 4/ sqrt 27
then i got
sqrt 108/ 27
then what?
help me!! gracias
What's the square root of 4, madelyn? 2, right?
so sqrt(4) / sqrt(27) = 2 / sqrt(27)

I'll let you finish it...

#### soroban

##### Elite Member

The question is: $$\displaystyle \L\,\frac{\sqrt{4}}{\sqrt{27 }}$$

then i got: $$\displaystyle \L\,\frac{\sqrt{108}}{27}\;$$ . . . right!

then what?
What you did is absolutely correct!

Now see if we can simplify $$\displaystyle \,\sqrt{108}$$

$$\displaystyle \;\;\sqrt{108}\;=\;\sqrt{36\cdot3}\;=\;\sqrt{36}\cdot\sqrt{3}\;=\;6\sqrt{3}$$

So we have: $$\displaystyle \L\,\frac{6\sqrt{3}}{27}\;=\;\frac{2\sqrt{3}}{9}$$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

It would be easier (I think) if you simplified first ... as Denis suggested.

You know that: $$\displaystyle \,\sqrt{4}\,=\,2$$

$$\displaystyle \;\;$$and that: $$\displaystyle \,\sqrt{27}\,=\,\sqrt{9\cdot3}\,=\,\sqrt{9}\cdot\sqrt{3}\,=\,3\sqrt{3}$$

So the problem becomes: $$\displaystyle \L\,\frac{2}{3\sqrt{3}}$$

Now rationalize: $$\displaystyle \L\,\frac{2}{3\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\:=\:\frac{2\sqrt{3}}{9}$$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Always simplify first . . . things usually work out much simpler.

Example: $$\displaystyle \L\,\frac{\sqrt{72}}{\sqrt{50}}$$

Instead of messing around with $$\displaystyle 50$$ and $$\displaystyle 3600$$, simplify!

$$\displaystyle \;\;\sqrt{72}\:=\:\sqrt{36\cdot2}\:=\:\sqrt{6}\sqrt{2}\:=\:6\sqrt{2}$$

$$\displaystyle \;\;\sqrt{50}\:=\:\sqrt{25\cdot2}\:=\:\sqrt{25}\cdot\sqrt{2}\:=\:5\sqrt{2}$$

The problem becomes: $$\displaystyle \L\;\frac{6\sqrt{2}}{5\sqrt{2}}\;=\;\frac{6}{5}\;\;$$ . . . see?