gahh help

[madelynnnnnn]

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

then what?

help me!! gracias

 

[Denis]

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]

Hello, madelynnnnnn!

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: \(\displaystyle \L\,\frac{6\sqrt{3}}{27}\;=\;\frac{2\sqrt{3}}{9}\)

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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: \(\displaystyle \L\,\frac{2}{3\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\:=\:\frac{2\sqrt{3}}{9}\)

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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?