Simplifying Radical Expressions

madelynnnnnn

New member
Joined
Apr 6, 2006
Messages
12
I sort of understand how to do this and sort of not. I like need an explanation of like each step cause I have more like this...

Example 1:

[sqrt(7)/sqrt(2)] times [sqrt(14)/sqrt(27)]

i think the next step is sqrt(98)/sqrt(54) and then i think you rationalize the denominator and get

sqrt(5292)/54

thankyou very very much for your help
 

daon

Senior Member
Joined
Jan 27, 2006
Messages
1,284
madelynnnnnn said:
I sort of understand how to do this and sort of not. I like need an explanation of like each step cause I have more like this...

Example 1:

[sqrt(7)/sqrt(2)] times [sqrt(14)/sqrt(27)]

i think the next step is sqrt(98)/sqrt(54) and then i think you rationalize the denominator and get

sqrt(5292)/54

thankyou very very much for your help
\(\displaystyle \frac{\sqrt{7}}{\sqrt{2}}\frac{\sqrt{14}}{\sqrt{27}} = \sqrt{\frac{7*14}{2*27}} = \sqrt{\frac{98}{54}} = \sqrt{\frac{49*27}{27*27}} = \frac{7\sqrt{27}}{27} = \frac{7\sqrt{9*3}}{27} = \frac{21\sqrt{3}}{27} = \frac{7\sqrt{3}}{9}\)
 

madelynnnnnn

New member
Joined
Apr 6, 2006
Messages
12
ok i have no idea where you got the sqrt (49*27) / (27*27)
i under stand everything up to there
 

daon

Senior Member
Joined
Jan 27, 2006
Messages
1,284
madelynnnnnn said:
ok i have no idea where you got the sqrt (49*27) / (27*27)
i under stand everything up to there
Sorry, I accidently combined two steps into one..

\(\displaystyle \sqrt{\frac{98}{54}} = \sqrt{\frac{49}{27}} = \sqrt{\frac{49*27}{27*27}}\)
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, madelynnnnnn!

\(\displaystyle \L\,\sqrt{\frac{7}{2}}\,\cdot\,\sqrt{\frac{14}{27}}\)
Before you "mash" them together, look for squares.

\(\displaystyle \L\;\;\sqrt{\frac{7\cdot14}{2\cdot27}}\;=\;\sqrt{\frac{7\cdot7\cdot\not{2}}{\not{2}\cdot9\cdot3}} \;= \;\sqrt{\frac{49}{9\cdot3}} \;=\;\frac{\sqrt{49}}{\sqrt{9}\cdot\sqrt{3}}\;=\;\frac{7}{3\sqrt{3}}\)


Rationalize the denominator: \(\displaystyle \L\:\frac{7}{3\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\;=\;\frac{7\sqrt{3}}{9}\)
 
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