Multiplying & Simplifying Radical Expression: (-5 sqrt[3])/(sqrt[6]) * (-sqrt[7])/...

[markl77]

Multiplying & Simplifying Radical Expression: (-5 sqrt[3])/(sqrt[6]) * (-sqrt[7])/...

\(\displaystyle \dfrac{-5\, \sqrt{\strut 3\,}}{\sqrt{\strut 6\,}}\, \times\, \dfrac{-1\, \sqrt{\strut 7\,}}{3\,\sqrt{\strut 21\,}}\)

I'm not quite sure how to simplify this...
my work so far is multiplying straight across which gives me

\(\displaystyle \dfrac{5\, \sqrt{\strut 21\,}}{3\,\sqrt{\strut 126\,}}\)

From here if I multiply by the bottom radical it just gives the wrong answer when I try to simplify it.
(honestly I have no idea to put the LaTex things in, sorry.)

 

[ksdhart2]

Well, you're on the right track. What you've done so far is good. Your proposed strategy of multiplying by the denominator will also work:

\(\displaystyle \dfrac{5\sqrt{21}}{3\sqrt{126}} = \dfrac{5\sqrt{21}}{3\sqrt{126}} \times \dfrac{3\sqrt{126}}{3\sqrt{126}} = \dfrac{5\sqrt{21} \times 3\sqrt{126}}{3\sqrt{126} \times 3\sqrt{126}}\)

Another way you might tackle it is to note that \(\displaystyle \dfrac{5\sqrt{21}}{3\sqrt{126}} = \dfrac{5\sqrt{21}}{3\sqrt{6 \times 21}}\) and proceed from there. Either way, we can't advise on where you might have gone wrong, because we can't troubleshoot work we can't see.

Also, your LaTeX is fine, but the code needs to be between \(\displaystyle brackets\)

 

[stapel]

\(\displaystyle \dfrac{-5\, \sqrt{\strut 3\,}}{\sqrt{\strut 6\,}}\, \times\, \dfrac{-1\, \sqrt{\strut 7\,}}{3\,\sqrt{\strut 21\,}}\)

I'm not quite sure how to simplify this...
my work so far is multiplying straight across which gives me

\(\displaystyle \dfrac{5\, \sqrt{\strut 21\,}}{3\,\sqrt{\strut 126\,}}\)

Maybe simplify as you go...?

. . . . .\(\displaystyle \dfrac{-5\, \sqrt{\strut 3\,}}{\sqrt{\strut 6\,}}\, \times\, \dfrac{-1\, \sqrt{\strut 7\,}}{3\,\sqrt{\strut 21\,}}\)

. . . . .\(\displaystyle \dfrac{-5\, \sqrt{\strut 3\,}}{\sqrt{\strut 3\,}\, \sqrt{\strut 2\,}}\, \times\, \dfrac{-1\, \sqrt{\strut 7\,}}{3\,\sqrt{\strut 7\,}\, \sqrt{\strut 3\,}}\)

. . . . .\(\displaystyle \left(\dfrac{\sqrt{\strut 3\,}\, \sqrt{\strut 7\,}}{\sqrt{\strut 3\,}\, \sqrt{\strut 7\,}}\right)\, \left(\dfrac{-5\, \times (-1)}{\sqrt{\strut 2\,}\, \times 3\, \sqrt{\strut 3\,}}\right)\)

. . . . .\(\displaystyle \dfrac{-5\, \times (-1)}{\sqrt{\strut 2\,}\, \times 3\, \sqrt{\strut 3\,}}\)

...and so forth.