#6**+15 **

Perhaps I should have included the following extra step:

\(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times\sqrt5\times\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}etc\)

i.e. you multiply the expression by 1 in the form \(\frac{\sqrt5}{\sqrt5}\) Then you multiply the two \(\sqrt5\)s on the bottom together.

Hope this explains it adequately for you.

.

Alan
Feb 18, 2017

#1**0 **

10/3sqrt5

(10/3)/((3sqrt5)/3)=

3.33/sqrt5

3.33^{2}/sqrt5^{2}=

11.11/5

11.11/5=20/9 so

10/3sqrt5=20/9

Scruffy23.
Feb 18, 2017

#2**0 **

wait i checked with calculator and this is wrong so i dont know where i slipped up

Scruffy23.
Feb 18, 2017

#8**+5 **

You did this:

\(\dfrac{3.33^2}{\sqrt5^2}\)

But you should take a square root after squaring both numerator and denominator......

Correct answer:

\(\sqrt{\dfrac{3.33^2}{\sqrt5^2}}\\ =\sqrt{\dfrac{100}{9}\cdot \dfrac{1}{5}}\\ =\sqrt{\dfrac{20}{9}}\\ =\dfrac{\sqrt{20}}{\sqrt9}\\ =\dfrac{\sqrt{20}}{3}\)

And knowing that \(\sqrt{20}=\sqrt{2^2\cdot 5}=2\sqrt 5\)

Final answer = \(\dfrac{2}{3}\sqrt 5\)

MaxWong
Feb 18, 2017

#3**+5 **

Like so: \(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}\rightarrow\frac{2\sqrt5}{3}\)

.

Alan
Feb 18, 2017

#5

#6**+15 **

Best Answer

Perhaps I should have included the following extra step:

\(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times\sqrt5\times\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}etc\)

i.e. you multiply the expression by 1 in the form \(\frac{\sqrt5}{\sqrt5}\) Then you multiply the two \(\sqrt5\)s on the bottom together.

Hope this explains it adequately for you.

.

Alan
Feb 18, 2017