simplifying a surd

[jackmac]

I need help in how to express my calulation

I've simplified the surd, but which way would you say is the best way of expressing it? the top, in which i multiply the numerator out and divide by 42, or the bottom, where i use reoccurring values and cancel them out, then simplify?

Method 1:

\(\displaystyle \dfrac{3\,\sqrt{14\,}}{\sqrt{42\,}}\,=\, \dfrac{\sqrt{9\,}\,\sqrt{2\,}\, \sqrt{7\,}}{\sqrt{42\,}}\)

. . . . . ..\(\displaystyle =\, \dfrac{\sqrt{126\,}}{\sqrt{42\,}}\, =\, \dfrac{\sqrt{3\,}}{\sqrt{1\,}}\, =\, \sqrt{3\,}\)

Method 2:

\(\displaystyle \dfrac{3\,\sqrt{14\,}}{\sqrt{42\,}}\,=\, \dfrac{\sqrt{9\,}\,\sqrt{2\,}\, \sqrt{7\,}}{\sqrt{3\,}\, \sqrt{2\,}\, \sqrt{7\,}}\)

. . . . . ..\(\displaystyle =\, \dfrac{\sqrt{9\,}}{\sqrt{3\,}}\, =\, \dfrac{\sqrt{3\,}}{\sqrt{1\,}}\, =\, \sqrt{3\,}\)

Thanks for your time

 

[jackmac]

I guess its just a case of 6 and 2 3's

Thanks for the advice

 

[jackmac]

Thanks for that I appreciate the experienced advice. I did decide to go with the second option anyways but your advice was most helpful for future reference

 

[Steven G]

I need help in how to express my calulation

I've simplified the surd, but which way would you say is the best way of expressing it? the top, in which i multiply the numerator out and divide by 42, or the bottom, where i use reoccurring values and cancel them out, then simplify?

Method 1:

\(\displaystyle \dfrac{3\,\sqrt{14\,}}{\sqrt{42\,}}\,=\, \dfrac{\sqrt{9\,}\,\sqrt{2\,}\, \sqrt{7\,}}{\sqrt{42\,}}\)

. . . . . ..\(\displaystyle =\, \dfrac{\sqrt{126\,}}{\sqrt{42\,}}\, =\, \dfrac{\sqrt{3\,}}{\sqrt{1\,}}\, =\, \sqrt{3\,}\)

Method 2:

\(\displaystyle \dfrac{3\,\sqrt{14\,}}{\sqrt{42\,}}\,=\, \dfrac{\sqrt{9\,}\,\sqrt{2\,}\, \sqrt{7\,}}{\sqrt{3\,}\, \sqrt{2\,}\, \sqrt{7\,}}\)

. . . . . ..\(\displaystyle =\, \dfrac{\sqrt{9\,}}{\sqrt{3\,}}\, =\, \dfrac{\sqrt{3\,}}{\sqrt{1\,}}\, =\, \sqrt{3\,}\)

Thanks for your time

Between the two ways you listed I like method 2. Which is best? That is a matter of your style. Here is how I would do this-
3sqrt(14)/sqrt(42) = 3/sqrt(3)= sqrt(3)

 

[Steven G]

Huh? Pls explain...

14/42= 1/3. 3/sqrt(3)=sqrt3*sqrt(3)/sqrt(3)=sqrt(3). I used the fact that 3=sqrt(3)*sqrt(3).