How does 9 / (14^1/2)(21^1/2) equal (3)(6^1/2) / 14 ?

[Lime]

How does this:

9 / (14^1/2)(21^1/2)

Equal this:

(3)(6^1/2) / 14

:?:

 

[Denis]

Re: Just a question

How does this: 9 / (14^1/2)(21^1/2)
Equal this: (3)(6^1/2) / 14

Hint: (14^1/2)(21^1/2) = sqrt(294) = sqrt(49*6) = 7sqrt(6)

 

[jonboy]

I'm confused here (I think cuz it's 11 : 36 p.m.)........

How does: \(\displaystyle \L \;\frac{9}{{(14^{\frac{1}{2}} )(21^{\frac{1}{2}} )}} = \frac{{(3)(6^{^{\frac{1}{2}} } )}}{{14}}\) ?

\(\displaystyle \L \;\frac{9}{{(14^{\frac{1}{2}} )(21^{\frac{1}{2}} )}}\,\Rightarrow\,\frac{9}{{(294)^{\frac{1}{2}} }}\,\to\,
\frac{{9}}{{\sqrt {(294)^{\frac{1}{2}} } }}\,\Rightarrow\,\frac{9}{7\sqrt{6}}\)

\(\displaystyle \L \;\frac{{(3)(6^{^{\frac{1}{2}} } )}}{{14}}\,=\,\frac{3sqrt{6}}{14}\,\)

Ok Denis got ya. Just had to know.

 

[Denis]

Jonboy, 3 * sqrt(6) does not equal sqrt(18) !

9 / 7sqrt(6) = 9sqrt(6) / 42 = 3sqrt(6) / 14

 

[Mrspi]

Re: Just a question

How does this:

9 / (14^1/2)(21^1/2)

Equal this:

(3)(6^1/2) / 14

:?:

Here's a slightly different approach:

14^1/2 = (2*7)^1/2, or (2^1/2)*(7^1/2)

21^1/2 = (3*7)^1/2, or (3^1/2)*(7^1/2)

So, 14^1/2*21^1/2 is the same thing as (2^1/2)*(3^1/2)*(7^1/2)^2
or,
7*(2^1/2)*(3^1/2)
7*(2*3)^1/2
7*(6^1/2)

Ok....now the fraction looks like this:

9 / [7*(6^1/2)]

Multiply numerator and denominator by 6^1/2 to rationalize the denominator:

9*(6^1/2)
-------------
7*6

Reduce the fraction, and you have

3*(6^1/2)
-------
14