+33615 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.
.
+247 10/3sqrt5
(10/3)/((3sqrt5)/3)=
3.33/sqrt5
3.332/sqrt52=
11.11/5
11.11/5=20/9 so
10/3sqrt5=20/9
+247 wait i checked with calculator and this is wrong so i dont know where i slipped up
+9519 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 = \(\dfrac{2}{3}\sqrt 5\)
+33615 Like so: \(\frac{10}{3\sqrt5}\rightarrow\frac{10\sqrt5}{3\times5}\rightarrow\frac{2\sqrt5}{3}\)
.
+33615 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.
.
